Stability Analysis for Class of Switched Nonlinear Systems

Abstract-Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. The results are illustrated by numerical examples

Diagonal Riccati Stability and Applications

We consider the question of diagonal Riccati stability for a pair of real matrices A, B. A necessary and sufficient condition for diagonal Riccati stability is derived and applications of this to two distinct cases are presented. We also describe some motivations for this question arising in the theory of generalised Lotka-Volterra systems

Output Feedback Control of Switched Nonlinear Systems: A Gain Scheduling Approach

Switched controller design for nonlinear continuous and discrete-time systems under an arbitrary switching signal using the gain scheduling approach is addressed in this paper. The obtained controller design procedures for continuous and discrete-time systems are in the bilinear matrix inequality form. The proposed design procedure ensures multi parameter-dependent quadratic stability of the switched gain scheduled plant which is associative to a nonlinear plant model and optimal performance defined by quadratic gain scheduled parameters weighting cost function. Example demonstrates the effectiveness of the proposed approaches

Complexity of risk determination

Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. The results are illustrated by numerical examples

Stability Analysis Of Lur'e-type Switched Systems

This technical note aims to introduce stability analysis of Lur'e-type switched systems in frequency domain. A new state-input dependent switching function is proposed and it is the key issue to obtain a stability condition that generalizes the celebrated Popov criterion to deal with this class of switched nonlinear systems. Likewise the case of time invariant systems, we propose a frequency domain stability test that is expressed through a convex combination of the subsystems state space matrices. This task is not trivial due to the time-varying nature of the nonlinear systems under consideration. The theory is illustrated by a simple example.591130463050Yu. Aleksandrov, A., Chen, Y., Platonov, A.V., Zhang, L., Stability analysis for a class of switched nonlinear systems (2011) Automatica, 47, pp. 2286-2291Branicky, M.S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems (1998) IEEE Trans. Autom. Control, 43, pp. 475-482Colaneri, P., Geromel, J.C., Astolfi, A., Stabilization of continuoustime switched nonlinear systems (2008) Syst. Control Lett., 57, pp. 95-103Deaecto, G.S., Geromel, J.C., Daafouz, J., Dynamic output feedback H? Control of switched linear systems (2011) Automatica, 47, pp. 1713-1720Decarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B., Perspectives and results on the stability and stabilizability of hybrid systems (2000) Proc IEEE, 88, pp. 1069-1082Geromel, J.C., Colaneri, P., Stability and stabilization of continuoustime switched linear systems (2006) SIAM J. Control Optim., 45, pp. 1915-1930Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Trans. Autom. Control, 53, pp. 720-733Geromel, J.C., Deaecto, G.S., Switched state feedback control for continuous-time uncertain systems (2009) Automatica, 45, pp. 593-597Geromel, J.C., Deaecto, G.S., Daafouz, J., Suboptimal switching control consistency analysis for switched linear systems (2013) IEEE Trans. Autom. Control, 58, pp. 1857-1861Hespanha, J.P., Uniform stability of switched linear systems: Extensions of LaSalle's principle (2004) IEEE Trans. Autom. Control, 49, pp. 470-482Ji, Z., Wang, L., Xie, G., Quadratic stabilization of switched systems (2005) Int. J. Syst. Sci., 36, pp. 395-404Liberzon, D., (2003) Switching in Systems and Control, , Boston MA: BirkhaüserLin, H., Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results (2009) IEEE Trans. Autom. Control, 54, pp. 308-322Long, L., Zhao, J., Global stabiization for a class of switched nonlinear feedforward systems (2011) Automatica, 60, pp. 734-738Moulay, E., Bourdais, R., Perruquetti, W., Stabilization of nonlinear switched systems using control Lyapunov functions (2007) Nonlin. Anal.: Hybrid Syst., 1, pp. 482-490Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C., Stability criteria for switched and hybrid systems (2007) SIAM Rev., 49, pp. 545-592Sun, Z., Ge, S.S., (2005) Switched Linear Systems: Control and Design, , London, U.K.: SpringerSun, Y., Wang, L., On stability of a class of switched nonlinear systems (2013) Automatica, 49, pp. 305-307Wu, J.-L., Stabilizing controllers design for switched nonlinear systems in strict-feedback form (2009) Automatica, 45, pp. 1092-1096Yang, H., Concquempot, V., Jiang, B., On stabilization of switched nonlinear systems with unstable modes (2009) Syst. Control Lett., 58, pp. 703-708Zhai, G., Quadratic stabilizability and H? Disturbance attenuation of switched linear systems via state and output feedback (2012) Proc IEEE Conf. Decision Control, pp. 1935-1940. , Maui, HI, USAZhao, J., Hill, D.J., On stability L2 gain andH? Control for switched systems (2008) Automatica, 44, pp. 1220-123