A new design of robust H∞ filters for uncertain continuous-time stochastic systems

This paper is concerned with the problemof robust H∞ filtering for linear continuoustimestochastic systems with polytopic parameteruncertainties. We utilize the polynomial parameterdependent approach to solve the robust H∞ filteringproblem, and the proposed approach include resultsin the quadratic framework that entail fixed matricesfor the entire uncertain domain and results in the linearlyparameter-dependent framework that use linearconvex combinations of matrices as special cases. Newlinear matrix inequality (LMI) conditions obtainedfor the existence of admissible for the existence ofadmissible filters are developed based on homogenouspolynomial parameter-dependent matrices of arbitrarydegree. Numerical examples are provided toillustrate the effectiveness and advantages of the filterdesign methods proposed in this paper

Robust H∞ Control of Takagi–Sugeno Systems with Actuator Saturation

Producción CientíficaThe robust static output feedback control for continuous-time Takagi–Sugeno systems subject to actuator saturation is solved here, including H∞ performance guarantees. Based on a polytopic model of the saturation, sufficient conditions are proposed for designing these controllers in terms of Linear Matrix Inequalities. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved easily without requiring iterative algorithms or equality constraints, moreover, the output matrix of the considered system does not require to be full row rank. Finally, some examples are presented to show the validity of the proposed methodology

A two dimensional fluid model for TCP/AQM analysis

This work proposes a new mathematical model for the TCP/AQM system that aims to improve the accuracy of existing fluid models, especially with respect to the sequential events that occur in the network. The analysis is based on the consideration of two time bases, one at the queue's router level and the other at the congestion window level, which leads to the derivation of a new nonlinear two-dimensional fluid model for Internet congestion control. To avoid the difficult task of assessing stability of a 2D nonlinear dynamic model, we perform a local stability analysis of a 2D linear TCP AQM model. By constructing a new two dimensional second order Bessel Legendre Lyapunov functional, new matrix inequalities are derived to evaluate the stability of the 0-input system and to synthesize a feedback controller. Finally, two Internet traffic scenarios, with state space matrices for replicability, are presented, demonstrating the validity of the theoretical results.Comment: Active queue management, network assisted congestion control, TCP/AQM, 2D time delay systems, Roesser model, 2D second order bessel Legendre, Lyapuno

POLYNOMIAL STATIC OUTPUT FEEDBACK H ∞ CONTROL FOR CONTINUOUS-TIME LINEAR SYSTEMS VIA DESCRIPTOR APPROACH

International audienceThis paper deals with the problem of the robust static output feedback H ∞ control (SOFC) for continuous linear systems with polytopic uncertainties. The controller has been gotten by the use of descriptor redundancy. Under this approach a sufficient condition is provided for the existence of a solution to the problem. Thus, the advantage of this method is to obtain more free matrices in the design condition, also the polynomial approach helps to have a less conservative result. In the end, the performance of the method is shown by several examples

Robust H∞ Filters for Uncertain Systems with Finite Frequency Specifications

International audienceThis paper deals with H∞ filtering problem of linear discrete-time uncertain systems with finite frequency input signals. The uncertain parameters are supposed to reside in a polytope. By applying the generalized Kalman–Yakubovich–Popov lemma, polynomially parameter-dependentLyapunov function and some key matrices to eliminate the product terms between the filter parameters and the Lyapunov matrices, an improved condition isobtained for analyzing the H∞performance of the filtering error system. Then sufficient condition in terms of linear matrix inequality is established for designing filters with a guaranteed H∞ filtering performance level. Finally, a numerical examples are used to demonstrate the effectiveness of the proposed method

Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

Producción CientíficaThe stabilization of Takagi–Sugeno systems is solved here for the two-dimensional polynomial discrete case, by using the sum-of-squares approach. First, we provide a stabilization condition formulated in terms of polynomial multiple Lyapunov functions. Then, a non-quadratic stabilization condition is developed by applying relaxed stabilization technique. Both conditions can be used for design, by solving them using numerical tools such as SOSTOOLS. A numerical example illustrates the effectiveness of the results.Junta de Castilla y León y EU-FEDER (CLU 2017-09) y (UIC 233)Secretaría de Estado de Investigación, Desarrollo e Innovación (Grant. DPI2014-54530-R

Two-dimensional systems: from introduction to state of the art

A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The problems of delay and saturation are treated at the same time. The authors obtain novel results on continuous 2-D systems using the unidirectional Lyapunov function. The control synthesis and the saturation and delay conditions are presented as linear matrix inequalities. Illustrative examples are worked through to show the effectiveness of the approach and many comparisons are made with existing results. The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems. Solutions for the filter-design problems are demonstrated by computer simulation. The text builds up to the development of state feedback control for 2-D Takagi–Sugeno systems with stochastic perturbation. Conservatism is reduced by using slack matrices and the coupling between the Lyapunov matrix and the system matrices is broken by using basis-dependent Lyapunov functions. Mean-square asymptotic stability and prescribed H-infinity performance are guaranteed. Two-Dimensional Systems emphasizes practical approaches to control and filter design under constraints that appear in real problems and uses off-the-shelf software to achieve its results. Researchers interested in control and filter design for multidimensional systems, especially multi-dimensional fuzzy systems, will find this book a useful resource as will graduate students specializing in dynamical sytems

Stability analysis of linear systems with time varying delay: An input output approach

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Delay Dependent Exponential Stability and Guaranteed Cost of Time-Varying Delay Singular Systems

This paper deals with the problem of delay-dependent guaranteed cost exponential stability of singular systems with time-varying delay. Some improved delaydependent conditions are presented, in the form of linear matrix inequalities to ensure the considered system to be regular, impulse free and exponentially stable with the existence of a guaranteed cost. Numerical examples are given to show the usefulness of the proposed results

Fault tolerant saturated control for T―S fuzzy discrete-time systems with delays

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