Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

Abstract

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time-varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly .Q; S; R/ dissipative. By introducing a novel augmented Lyapunov-Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H 1 performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. n 2 OE0; 1/ stands for the space of n-dimensional square integrable function over OE0; 1/; a positive definite matrix P is denoted by P > 0; I is the unit matrix with appropriate dimension, and means symmetric term in the symmetric matrix.

Finite‐Time Nonfragile Dissipative Filter Design for Wireless Networked Systems with Sensor Failures

“…Definition (see [26]). The augmented filtering system (8) is (Q, S, R) − dissipative with respect to…”

“…A new criterion of stability analysis for generalized neural networks subject to time-varying delayed signals is investigated in [25]. By employing the LMI approach, a new set of sufficient conditions is obtained in [26] for the existence of reliable dissipative filter which makes the filtering error system stochastically stable and strictly (Q, S, R)-dissipative.…”

Feedback stabilization of multi‐DOF nonlinear stochastic Markovian jump systems

“…The early research concentrated mainly on the linear MJSs. During the recent years, a large number of research activities have been concerned on the nonlinear MJSs . For example, sliding mode control is extended to robust stabilization of nonlinear MJSs and the ergodic control problem of nonlinear MJSs is studied based on the dynamic programming principle .…”

“…During the recent years, a large number of research activities have been concerned on the nonlinear MJSs. [11][12][13][14][15][16][17][18] For example, sliding mode control is extended to robust stabilization of nonlinear MJSs 19,20 and the ergodic control problem of nonlinear MJSs is studied based on the dynamic programming principle. 21,22 However, most of the work done on stabilization and control is built upon the assumption of the MJSs without stochastically driven.…”

Stabilization of Discrete-Time Markovian Jump Systems by a Partially Mode-Unmatched Fault-Tolerant Controller

“…It also has been widely studied in the field of industrial process control, space flight, medical treatment, electric power and economy. During the past few decades, many important results based on kinds of systems have emerged, such as stability analysis [1][2][3][4][5][6], stabilization [7][8][9][10], delay case [11][12][13], output control [14,15], H ∞ control [16][17][18][19] and filtering [20][21][22], robust control [23][24][25], sliding control [26], state estimation [27], fault detection [28], synchronization [29,30], and so on.…”