Mode-independent H2-control of a DC motor modeled as a Markov jump linear system

This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H2 -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that of a previous design, and its usefulness is illustrated by an application that considers the velocity control of a DC motor device subject to abrupt failures that is modeled as an MJLS

H2 Control For Discrete-time Systems Optimality And Robustness

This paper proposes a new approach to determine H2 optimal control for discrete-time linear systems, based on convex programming. It is shown that all stabilizing state feedback control gains belong to a certain convex set, well-defined in a special parameter space. The Linear Quadratic Problem can be then formulated as the minimization of a linear objective over a convex set. The optimal solution of this convex problem furnishes, under certain conditions, the same feedback control gain which is obtained from the classical discrete-time Riccati equation solution. Furthermore, the method proposed can also handle additional constraints, for instance, the ones needed to assure asymptotical stability of discrete-time systems under actuators failure. Some examples illustrate the theory. © 1992.291225228Anderson, Moore, (1971) Linear Optimal Control, , Prentice Hall, Englewood Cliffs, NJBernussou, Peres, Geromel, A linear programming oriented procedure for quadratic stabilization of uncertain systems (1989) Systems and Control Letters, 13, pp. 65-72Dorato, Levis, Optimal linear regulators the discrete time case (1971) IEEE Transactions on Automatic Control, 16, pp. 613-620Geromel, Peres, Bernussou, On a convex parameter space method for linear control design of uncertain systems (1991) SIAM J. on Control and Optimiz., 29, pp. 381-402Kwakernaak, Sivan, (1972) Linear Optimal Control Systems, , John Wiley, New YorkLuenberger, (1973) Introduction to Linear Programming, , Addison-Wesley, Reading, M

Global Optimization For The H2-norm Model Reduction Problem And The H2-norm Controller Reduction Problem [otimização Global Para Os Problemas De Redução H2 De Modelos E Redução H2 Da Ordem Do Controlador]

A branch and bound algorithm is proposed to solve the H2-norm model reduction problem and the H2-norm controller reduction problem, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through linear matrix inequalities formulations. Examples illustrate the results.12293101Assunção, E., (2000) Redução H2 e H∞ de Modelos Através de Desigualdades Matriciais Lineares: Otimiação Local e Global, , Tese de Doutorado, UNICAMP, Campinas, SPAssunção, E., Peres, P.L.D., Redução de modelos com critério H∞ através de desigualdades matriciais lineares: Casos contínuo e discreto no tempo (1998) XII Congresso Brasileiro de Automática, 3, pp. 885-890. , Uberlândia, MGAssunção, E., Peres, P.L.D., Redução de modelos contínuos com critério H2 através de desigualdades matriciais lineares (1998) XII Congresso Brasileiro de Automática, 3, pp. 879-884. , Uberlândia, MGAssunção, E., Peres, P.L.D., Redução de modelos discretos com critério H2 através de desigualdades matriciais lineares (1998) VIII Latin American Congress on Automatic Control, 1, pp. 61-66. , Viña del Mar, ChileAssunção, E., Peres, P.L.D., A global optimization approach for the H2-norm model reduction problem (1999) Proceedings of the 38th IEEE Conference on Decision and Control, pp. 1857-1862. , Phoenix, AZ, USAAssunção, E., Peres, P.L.D., A H2 and/or H∞- norm model reduction of uncertain discrete-time systems (1999) Proceedings of the 1999 America, Control Conference, pp. 4466-4470. , San Diego, CA, USABalakrishnan, V., Boyd, S., Global optimization in control system analysis and design (1992) Control and Dynamic Systems: Advances in Theory and Applications, 53. , C. T. Leondes (ed.), Academic Press, New York, NYBalakrishnan, V., Boyd, S., Balemi, S., Branch and bound algorithm for computing the minimum stability degree of parameter-dependent linear systems (1991) International Journal of Robust and Nonlinear Control, 1 (4), pp. 295-317Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in Systems and Control Theory, , SIAM Studies in Applied Mathematics, USADorf, R.C., Bishop, R.H., (1995) Modern Control Systems, , Addison-Wesley Publishing Company, Reading, MassachusettsGahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., (1995) LMI Control Toolbox User's Guide, , The Mathworks Inc.,Natick, MA, USAGahinet, P., Nemirovskii, A., General-purpose LMI solvers with benchmarks (1994) Proceedings of the 32nd IEEE Conference on Decision and Control, 3, pp. 3162-3165. , San Antonio, TX, USAGlover, K., All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds (1984) International Journal of Control, 39 (6), pp. 1115-1193Goh, K.C., Safonov, M.G., Papavassilopoulos, G.P., A global optimization approach for the BMI problem (1994) Proceedings of the 33rd IEEE Conference on Decision and Control, pp. 2009-2014. , Lake Buena Vista, FL, USAGrigoriadis, K.M., L2 and L2 - L∞ model reduction via linear matrix inequalities (1997) International Journal of Control, 68 (3), pp. 485-498Helmersson, A., Model reduction using LMIs (1994) Proceedings of the 33rd IEEE Conference on Decision and Control, 4, pp. 3217-3222. , Lake Buena Vista, FL, USAJoshi, S.M., Kelkar, A.G., Inner loop control of supersonic aircraft in the presence of aeroelastic modes (1998) IEEE Transactions on Control Systems Technology, 6 (6), pp. 730-739Maranas, C.D., Floudas, C.A., Global optimization in generalized geometric programming (1997) Computers & Chemical Engineering, 21 (4), pp. 351-369Moore, B.C., Principal component analysis in linear systems: Controllability, observability, and model reduction (1981) IEEE Transactions on Automatic Control, AC-26 (1), pp. 17-32Ryoo, H.S., Sahinidis, N.V., Global optimization of nonconvex NLPs and MINLPs with applications in process design (1995) Computers & Chemical Engineering, 19 (5), pp. 551-566Valentin, C., Duc, G., LMI-based algorithms for frequency weighted optimal H2-norm model reduction (1997) Proceedings of the 36th IEEE Conference on Decision and Control, 1, pp. 767-772. , San Diego, CA, USAVanAntwerp, J.G., Braatz, R.D., A tutorial on linear and bilinear matrix inequalities (2000) Journal of Process Control, 10, pp. 363-385VanAntwerp, J.G., Braatz, R.D., Sahinidis, N.V., Globally optimal robust control of large scale sheet and film processes (1997) Proceedings of the 1997 American Control Conference, 3, pp. 1473-1477. , Albuquerque, New Mexico, US

Alternate Numerical Solution To The Linear Quadratic Problem

This note proposes a new method, based on convex programming, for solving the Linear Quadratic Problem (LQP) directly on the parameter space generated by the feedback control gain. All stabilizing controllers are mapped into a convex set; the problem is then formulated as a minimization of a linear function over this convex set. Its optimal solution furnishes, under certain conditions, the same feedback control gain obtained from the classical Riccati equation. Generalizations to decentralized control and output feedback control design are included. The theory is illustrated by some numerical examples.39119820

Decentralised Load-frequency Control

We propose a numerical procedure to determine the load-frequency control of a power system composed of several interconnected areas. In order to decrease the associated implementation cost, the control law is constrained to have two different special structures: decentralized feedback and/or output feedback control. The procedure is based on a new property of the classical Raccati equation which is analyzed in two different aspects: closed-loop asymptotic stability and suboptimality degree. An example of two interconnected areas is solved and comparisons are made in order to evaluate the performance of the closed-loop system.132522523

A Zero Padding Svd Encoder To Compress Electrocardiogram

[No abstract available]434Brandeis UniversityWei, J.-J., Chang, C.-J., Chou, N.-K., Jan, G.-J., ECG data compression using truncated singular value decomposition (2001) IEEE Transactions on Information Technology in Biomedicine, 5 (4), pp. 290-299. , De

Robust Pole Location By Parameter Dependent State Feedback Control

Sufficient conditions are given for the existence of a parameter dependent state feedback control assuring to a linear uncertain closed-loop system the pole location inside a circle in the complex plane. The uncertainties are supposed to belong to a polytope domain described by its vertices. The robust stabilizability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope. Extensions to cope with decentralized and output feedback parameter dependent control gains are also presented. Examples illustrate the results.218641869Barmish, B.R., (1994) New Tools for Robustness of Linear Systems, , Macmillan Publishing Company, New York, NY, USABernussou, J., Peres, P.L.D., Geromel, J.C., A linear programming oriented procedure for quadratic stabilization of uncertain systems (1989) Systems & Control Letters, 13 (1), pp. 65-72. , JulyBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., Linear matrix inequalities in system and control theory (1994) SIAM Studies in Applied Mathematics, , Philadelphia, USADahleh, M., Dahleh, M.A., On slowly time-varying systems (1991) Automatica, 27 (1), pp. 201-205. , JanuaryDe Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems & Control Letters, 37 (4), pp. 261-265. , JulyFeron, E., Apkarian, P., Gahinet, P., Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions (1996) IEEE Transactions on Automatic Control, 41 (7), pp. 1041-1046. , JulyGahinet, P., Apkarian, P., Chilali, M., Affine parameter-dependent Lyapunov functions and real parametric uncertainty (1996) IEEE Transactions on Automatic Control, 41 (3), pp. 436-442. , MarchHaddad, W.M., Bernstein, D.S., Controller design with regional pole constraints (1992) IEEE Transactions on Automatic Control, 57 (1), pp. 54-69. , JanuaryLeith, D.J., Leithead, W.E., Survey of gain-scheduling analysis and design (2000) International Journal of Control, 73 (11), pp. 1001-1025. , JulyRamos, D.C.W., Peres, P.L.D., A less conservative LMI condition for the robust stability of discrete-time uncertain systems (2001) Systems & Control Letters, 43 (5), pp. 371-378. , AugustRamos, D.C.W., Peres, P.L.D., An LMI approach to compute robust stability domains for uncertain linear systems (2002) IEEE Transactions on Automatic Control, 47 (4), pp. 675-678. , AprilRugh, W.J., Shamma, J.S., Research on gain scheduling (2000) Automatica, 36 (10), pp. 1401-1425. , OctoberSolo, V., On the stability of slowly time-varying linear-systems (1994) Mathematics of Control Signals and Systems, 7 (4), pp. 331-35

Lmi Relaxations For Reduced-order Robust H ∞ Control Of Continuous-time Uncertain Linear Systems

This technical note is concerned with the problem of reduced order robust H ∞ dynamic output feedback control design for uncertain continuous-time linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all the system matrices. The search for a reduced-order controller is converted in a problem of static output feedback control design for an augmented system. To solve the problem, a two-stage linear matrix inequality (LMI) procedure is proposed. At the first step, a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined. This parameter-dependent state feedback controller is used at the second stage, which synthesizes the robust (parameter- independent) output feedback H ∞ dynamic controller. A homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability with a prescribed H ∞ attenuation level. As illustrated by numerical examples, the proposed method provides better results than other LMI based conditions from the literature. © 2011 IEEE.57615321537Syrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback-A survey (1997) Automatica, 33 (2), pp. 125-137. , FebBlondel, V.D., Tsitsiklis, J.N., A survey of computational complexity results in systems and control (2000) Automatica, 36 (9), pp. 1249-1274. , SepFu, M., Luo, Z.-Q., Computational complexity of a problem arising in fixed order output feedback design (1997) Systems and Control Letters, 30 (5), pp. 209-215. , PII S0167691197000145Peres, P.L.D., Geromel, J.C., An alternate numerical solution to the linear quadratic problem (1994) IEEE Trans. Autom. Control, 39 (1), pp. 198-202. , JanGeromel, J.C., Peres, P.L.D., Souza, S.R., Convex analysis of output feedback control problems: Robust stability and performance (1996) IEEE Transactions on Automatic Control, 41 (7), pp. 997-1003. , PII S0018928696037129El Ghaoui, L., Oustry, F., AitRami, M., A cone complementarity linearization algorithm for static output-feedback and related problems (1997) IEEE Transactions on Automatic Control, 42 (8), pp. 1171-1176. , PII S0018928697042797Geromel, J.C., De Souza, C.C., Skelton, R.E., Static output feedback controllers: Stability and convexity (1998) IEEE Transactions on Automatic Control, 43 (1), pp. 120-125. , PII S0018928698011854Crusius, C.A.R., Trofino, A., Sufficient LMI conditions for output feedback control problems (1999) IEEE Trans. Autom. Control, 44 (5), pp. 1053-1057. , MayShaked, U., An LPD approach to robust and static output-feedback design (2003) IEEE Trans. Autom. Control, 48 (5), pp. 866-872. , MayGeromel, J.C., Korogui, R.H., Bernussou, J., Robust output feedback control for continuous time polytopic systems (2007) IET Control Theory Appl., 1 (5), pp. 1541-1549. , SepYaesh, I., Shaked, U., Robust reduced-order output-feedback control (2009) Proc. 6th IFAC Symp. Robust Control Design, Haifa, Israel, pp. 155-160. , JunTrofino, A., Sufficient LMI conditions for the design of static and reduced order controllers (2009) Proc. 48th IEEE Conf. Decision Control-28th Chinese Control Conf., pp. 6668-6673. , Shanghai, China DecHenrion, D., Lasserre, J.-B., Convergent relaxations of polynomial matrix inequalities and static output feedback (2006) IEEE Transactions on Automatic Control, 51 (2), pp. 192-202. , DOI 10.1109/TAC.2005.863494Apkarian, P., Noll, D., Nonsmooth synthesis (2006) IEEE Trans. Autom. Control, 51 (1), pp. 71-86. , JanGumussoy, S., Henrion, D., Millstone, M., Overton, M.L., Multiobjective robust control with HIFOO 2.0 (2009) Proc. 6th IFAC Symp. Robust Control Design, pp. 144-149. , www.cs.nyu.edu/overton/software/hifoo, Haifa, Israel Jun. [Online]. Available:Peaucelle, D., Arzelier, D., An efficient numerical solution for static output feedback synthesis (2001) Proc. Eur. Control Conf., pp. 3800-3805. , Porto, Portugal SepArzelier, D., Peaucelle, D., Salhi, S., Robust static output feedback stabilization for polytopic uncertain systems: Improving the guaranteed performance bound (2003) Proc. 4th IFAC Symp. Robust Control Design, pp. 425-430. , Milan, Italy JunMehdi, D., Boukas, E.K., Bachelier, O., Static output feedback design for uncertain linear discrete time systems (2004) IMA J. Math. Control Inform., 21 (1), pp. 1-13. , MarArzelier, D., Gryazina, E.N., Peaucelle, D., Polyak, B.T., Mixed LMI/Randomized methods for static output feedback control design: Stability and performance (2009) LAAS-CNRS, Tech. Rep., , SepArzelier, D., Gryazina, E.N., Peaucelle, D., Polyak, B.T., Mixed LMI/Randomized methods for static output feedback control design (2010) Proc. Amer. Control Conf., pp. 4683-4688. , Baltimore, MD, Jun./JulAgulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., Robust static output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains (2010) Proc. Amer. Control Conf., pp. 4677-4682. , Baltimore, MD, Jun./JulMoreira, H.R., Oliveira, R.C.L.F., Peres, P.L.D., Robust static output feedback design starting from a parameter-dependent state feedback controller for time-invariant discrete-time polytopic systems (2011) Optim. Control Appl. Meth., 32 (1), pp. 1-13. , Jan./FebAgulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., Static output feedback control of polytopic systems using polynomial Lyapunov functions (2010) Proc. 49th IEEE Conf. Decision Control, pp. 6894-6901. , Atlanta, GA, DecGahinet, P., Apkarian, P., A linear matrix inequality approach to control (1994) Int. J. Robust Nonlin. Control, 4 (4), pp. 412-448. , Jul./Au

On A Convex Parameter Space Method For Linear Control Design Of Uncertain Systems

This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors' knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.29238140

H∞ And H2 Nonquadratic Stabilisation Of Discrete-time Takagi-sugeno Systems Based On Multi-instant Fuzzy Lyapunov Functions

The problem of state feedback control design for discrete-time Takagi-Sugeno (TS) (T-S) fuzzy systems is investigated in this paper. A Lyapunov function, which is quadratic in the state and presents a multi-polynomial dependence on the fuzzy weighting functions at the current and past instants of time, is proposed.This function contains, as particular cases, other previous Lyapunov functions already used in the literature, being able to provide less conservative conditions of control design for TS fuzzy systems. The structure of the proposed Lyapunov function also motivates the design of a new stabilising compensator for Takagi-Sugeno fuzzy systems. The main novelty of the proposed state feedback control law is that the gain is composed of matrices with multi-polynomial dependence on the fuzzy weighting functions at a set of past instants of time, including the current one. The conditions for the existence of a stabilising state feedback control law that minimises an upper bound to the H∞ or H2 norms are given in terms of linear matrix inequalities. Numerical examples show that the approach can be less conservative and more efficient than other methods available in the literature.4617687Ariño, C., Sala, A., Design of multiple-parameterisation pdc controllers via relaxed conditions for multi-dimensional fuzzy summations (2007) Proceedings of the 2007 IEEE International Conference on Fuzzy Systems, pp. 1-6. , London, UKAriño, C., Sala, A., Relaxed lmi conditions for closed-loop fuzzy systems with tensor-product structure (2007) Engineering Applications of Artificial Intelligence, 20 (8), pp. 1036-1046Barbosa, K.A., De Souza, C.E., Trofino, A., Robust Filtering for Discrete-Time Uncertain Linear Systems Using Parameter-Dependent Lyapunov Functions (2002) Proceedings of the 2002 American Control Conference, pp. 3224-3229. , Anchorage, AK, USABernal, M., Guerra, T.M., Generalized nonquadratic stability of continuous-time takagi-sugeno models (2010) IEEE Transactions on Fuzzy Systems, 18 (4), pp. 815-822Bliman, P.-A., A convex approach to robust stability for linear systems with uncertain scalar parameters (2004) SIAM Journal on Control and Optimization, 42 (6), pp. 2016-2042Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, PA: SIAM Studies in Applied MathematicsCao, Y., Frank, P.M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach (2000) IEEE Transactions on Fuzzy Systems, 8 (2), pp. 200-211Cao, S.G., Rees, N.W., Feng, G., Further results about quadratic stability of continuous-time fuzzy control systems (1997) International Journal of Systems Science, 28 (4), pp. 397-404Chang, W.-J., Ku, C.C., Chang, W., Analysis and synthesis of discrete nonlinear passive systems via affine t-s fuzzy models (2008) International Journal of Systems Science, 39 (8), pp. 809-821Chang, X.-H., Yang, G.-H., Relaxed stabilization conditions for continuous-time takagi-sugeno fuzzy control systems (2010) Information Sciences, 180 (17), pp. 3273-3287Chang, X.-H., Yang, G.-H., Wang, H., Observer-based-control for discrete-time t-s fuzzy systems (2011) International Journal of Systems Science, 42 (10), pp. 1801-1809Chesi, G., Garulli, A., Tesi, A., Vicino, A., Polynomially parameter-dependent lyapunov functions for robust stability of polytopic systems: An lmi approach (2005) IEEE Transactions on Automatic Control, 50 (3), pp. 365-370Choi, D.J., Park, P., State-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent lyapunov functions (2003) IEEE Transactions on Fuzzy Systems, 11 (2), pp. 271-278Daafouz, J., Bernussou, J., Parameter dependent lyapunov functions for discrete time systems with time varying parameter uncertainties (2001) Systems & Control Letters, 43 (5), pp. 355-359Daafouz, J., Bernussou, J., Poly-quadratic stability and performance for discrete systems with time varying uncertainties (2001) Proceedings of the 40th IEEE Conference on Decision and Control, 1, pp. 267-272. , Orlando, FL, USADe Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D., Swevers, J., Gain-scheduled and control of discrete-time polytopic time-varying systems (2010) IET Control Theory & Applications, 4 (3), pp. 362-380Ding, B., Stabilization of takagi-sugeno model via non-parallel distributed compensation law (2010) IEEE Transactions on Fuzzy Systems, 18 (1), pp. 188-194Ding, B., Huang, B., Reformulation of lmi-based stabilisation conditions for non-linear systems in takagi-sugeno's form (2008) International Journal of Systems Science, 39 (5), pp. 487-496Ding, B., Sun, H., Yang, P., Further studies on lmi-based relaxed stabilization conditions for nonlinear systems in takagi-sugeno's form (2006) Automatica, 42 (3), pp. 503-508Dong, H., Wang, Z., Lam, J., Gao, H., Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts (2012) IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 42 (2), pp. 365-376Fang, C.-H., Liu, Y.-S., Kau, S.-W., Hong, L., Lee, C.-H., A new lmi-based approach to relaxed quadratic stabilization of t-s fuzzy control systems (2006) IEEE Transactions on Fuzzy Systems, 14 (3), pp. 386-397Gahinet, P., Nemirovskii, A., Laub, A.J., Chilali, M., (1995) LMI Control Toolbox User's Guide, , Natick, MA: The Math WorksGao, H., Zhao, Y., Chen, T., Fuzzy control of nonlinear systems under unreliable communication links (2009) IEEE Transactions on Fuzzy Systems, 17 (2), pp. 265-278Green, M., Limebeer, D.J.N., (1995) Linear Robust Control, , Englewood Cliffs, NJ: Prentice-HallGuerra, T.M., Bernal, M., A way to escape from the quadratic framework (2009) Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, pp. 784-789. , Jeju Island, KoreaGuerra, T.M., Bernal, M., Jaadari, A., Non-quadratic stabilization of takagi-sugeno models: A local point of view (2010) Proceedings of the 2010 IEEE International Conference on Fuzzy Systems, pp. 2375-2380. , Barcelona, SpainGuerra, T.M., Kruszewski, A., Bernal, M., Control law proposition for the stabilization of discrete takagi-sugeno models (2009) IEEE Transactions on Fuzzy Systems, 17 (3), pp. 724-731Guerra, T.M., Vermeiren, L., LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi-sugeno's form (2004) Automatica, 40 (5), pp. 823-829Huang, Y.-S., Huang, Z.-X., Zhou, D.-Q., Chen, X.-X., Zhu, Q.-X., Yang, H., Decentralised indirect adaptive output feedback fuzzy tracking design for a class of large-scale nonlinear systems (2012) International Journal of Systems Science, 43 (1), pp. 180-191Katayama, H., Ichikawa, A., Control for discrete-time takagi-sugeno fuzzy systems (2002) International Journal of Systems Science, 33 (14), pp. 1099-1107Kchaou, M., Souissi, M., Toumi, A., A new approach to non-fragile observer-based control for discrete-time fuzzy systems (2012) International Journal of Systems Science, 43 (1), pp. 9-20Kim, E., Lee, H., New approaches to relaxed quadratic stability condition of fuzzy control systems (2000) IEEE Transactions on Fuzzy Systems, 8 (5), pp. 523-534Kim, S.H., Park, P., State-feedback control design for fuzzy systems using lyapunov functions with quadratic dependence on fuzzy weighting functions (2008) IEEE Transactions on Fuzzy Systems, 16 (6), pp. 1655-1663Kruszewski, A., Guerra, T.M., New approaches for the stabilization of discrete takagi-sugeno fuzzy models (2005) Proceedings of the 44th IEEE Conference on Decision and Control-European Control Conference ECC 2005, pp. 3255-3260. , Seville, SpainKruszewski, A., Wang, R., Guerra, T.M., Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models: A new approach (2008) IEEE Transactions on Automatic Control, 53 (2), pp. 606-611Lam, H.K., Leung, F.H.F., LMI-based stability and performance conditions for continuous-time nonlinear systems in takagi-sugeno's form (2007) IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 37 (5), pp. 1396-1406Lam, J., Zhou, S., Dynamic output feedback h ∞ control of discrete-time fuzzy systems: Afuzzy-basis-dependent lyapunov function approach (2007) International Journal of Systems Science, 38 (1), pp. 25-37Lee, J.-W., On uniform stabilization of discrete-time linear parameter-varying control systems (2006) IEEE Transactions on Automatic Control, 51 (10), pp. 1714-1721Lee, D.H., Park, J.B., Joo, Y.H., Improvement on nonquadratic stabilization of discrete-time takagi-sugeno fuzzy systems: Multiple-parameterization approach (2010) IEEE Transactions on Fuzzy Systems, 18 (2), pp. 425-429Lee, D.H., Park, J.B., Joo, Y.H., Approaches to extended non-quadratic stability and stabilization conditions for discrete-time takagi-sugeno fuzzy systems (2011) Automatica, 47 (3), pp. 534-538Lee, D.H., Park, J.B., Joo, Y.H., Further improvement of periodic control approach for relaxed stabilization condition of discrete-time takagi-sugeno fuzzy systems (2011) Fuzzy Sets and Systems, 174 (1), pp. 50-65Lee, D.H., Park, J.B., Joo, Y.H., Further theoretical justification of the k-samples variation approach for discrete-time takagi-sugeno fuzzy systems (2011) IEEE Transactions on Fuzzy Systems, 19 (3), pp. 594-597Liu, J., Gu, Z., Tian, E., Yan, R., New results on h ∞ filter design for nonlinear systems with time-delay through a t-s fuzzy model approach (2012) International Journal of Systems Science, 43 (3), pp. 426-442Löfberg, J., YALMIP: A toolbox for modeling and optimization in matlab (2004) Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design, pp. 284-289. , http://control.ee.ethz.ch/joloef/yalmip.php, Taipei, TaiwanMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Convergent lmi relaxations for quadratic stabilizability and h ∞ control for takagi-sugeno fuzzy systems (2009) IEEE Transactions on Fuzzy Systems, 17 (4), pp. 863-873Mozelli, L.A., Palhares, R.M., Avellar, G.S.C., A systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems (2009) Information Sciences, 179 (8), pp. 1149-1162Oliveira, R.C.L.F., Peres, P.L.D., Parameter-dependent lmis in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via lmi relaxations (2007) IEEE Transactions on Automatic Control, 52 (7), pp. 1334-1340Sala, A., Ariño, C., Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of polya's theorem (2007) Fuzzy Sets and Systems, 158 (24), pp. 2671-2686Stoorvogel, A.A., The robust h2 control problem: A worst-case design (1993) IEEE Transactions on Automatic Control, 38 (9), pp. 1358-1370Sturm, J.F., Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones (1999) Optimization Methods and Software, 11 (1-4), pp. 625-653. , http://sedumi.mcmaster.ca/Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control (1985) IEEE Transactions on Systems, Man, and Cybernetics. SMC, 15 (1), pp. 116-132Tanaka, K., Hori, T., Wang, H.O., A multiple lyapunov function approach to stabilization of fuzzy control systems (2003) IEEE Transactions on Fuzzy Systems, 11 (4), pp. 582-589Tanaka, K., Ikeda, T., Wang, H.O., Fuzzy regulators and fuzzy observers: Relaxed stability conditions and lmi-based designs (1998) IEEE Transactions on Fuzzy Systems, 6 (2), pp. 250-265Tanaka, K., Ohtake, H., Wang, H.O., A descriptor system approach to fuzzy control system design via fuzzy lyapunov functions (2007) IEEE Transactions on Fuzzy Systems, 15 (3), pp. 333-341Tanaka, K., Wang, H., (2001) Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, , New York: John Wiley & SonsTeixeira, M.C.M., Assunção, E., Avellar, R.G., On relaxed lmi-based designs for fuzzy regulators and fuzzy observers (2003) IEEE Transactions on Fuzzy Systems, 11 (5), pp. 613-623Tognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D., Improved stabilization conditions for takagi-sugeno fuzzy systems via fuzzy integral lyapunov functions (2011) Proceedings of the 2011 American Control Conference, pp. 4970-4975. , San Francisco, CA, USATognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D., Selective h2 and h ∞ stabilization of takagi-sugeno fuzzy systems (2011) IEEE Transactions on Fuzzy Systems, 19 (5), pp. 890-900Tognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D., Reduced-order dynamic output feedback control of continuous-time t-s fuzzy systems (2012) Fuzzy Sets and Systems, 207, pp. 27-44Wang, H.O., Tanaka, K., Griffin, M.F., An approach to fuzzy control of nonlinear systems: Stability and design issues (1996) IEEE Transactions on Fuzzy Systems, 4 (1), pp. 14-23Wu, H.-N., Cai, K.-Y., H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty (2006) Automatica, 42 (7), pp. 1183-1188Yoneyama, J., Nishikawa, M., Katayama, H., Ichikawa, A., H ∞ control for takagi-sugeno fuzzy systems (2001) International Journal of Systems Science, 32 (7), pp. 915-924Zhou, S., Feng, G., Generalised h2 controller synthesis for uncertain discrete-time fuzzy systems via basis-dependent lyapunov functions (2006) IEE Proceedings-Control Theory and Applications, 153 (1), pp. 74-80Zhou, S., Feng, G., Lam, J., Xu, S., Robust h ∞ control for discrete-time fuzzy systems via basis-dependent lyapunov functions (2005) Information Sciences, 174 (3-4), pp. 197-217Zhou, S., Lam, J., Zheng, W.X., Control design for fuzzy systems based on relaxed nonquadratic stability and h ∞ performance conditions (2007) IEEE Transactions on Fuzzy Systems, 15 (2), pp. 188-19