RobustH_∞filtering for a class of uncertain stochastic hybrid neutral systems with time‐varying delay

Abstract

This paper is devoted to the problem of robust H 1 filtering for a class of uncertain switched neutral systems subject to stochastic disturbance and time-varying delay. Attention is focused on the design of a full-order switched filter such that the filtering error system is robust mean-square exponentially stable with a prescribed weighted H 1 performance. On the basis of the average dwell time approach and the piecewise Lyapunov function technique, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities. Then, by solving the corresponding linear matrix inequalities, the desired full-order switched filter is derived for all admissible uncertainties, time-varying delay, and stochastic disturbances. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright ROBUST H 1 FILTERING 463 as well as practical applications, analysis and synthesis of these systems have gained considerable attention [7][8][9][10][11]. Moreover, the filtering problem has also been investigated for continuous-time and discrete-time switched systems [12][13][14][15], respectively. Recently, because stochastic modeling comes to play a key role in many real systems, much important progress is made on the stochastic hybrid systems [16][17][18][19]. Some papers on the filtering problem for these systems are investigated in [20][21][22][23][24]. The authors in [21] study H 1 filtering problem for stochastic systems with Markovian switching. On the basis of the switched Lyapunov function method, the H 1 filtering problem for discretetime switched systems with missing measurements is considered in [23]. In [24], reduced-order L 2 L 1 filtering problem is investigated for switched stochastic systems without uncertainties and time delays.On the other hand, it has been shown that many practical systems can be modeled by using functional differential equations of the neutral type. As for these more general class systems involving the derivative of the delayed state, the stability analysis and synthesis issues are proved to be much more difficult than those of the retarded type. Such kind of delay systems with the neutral type in both the deterministic and stochastic cases have been studied [25][26][27][28]. For instance, the problems of stability and stochastic stability for neutral systems are investigated in [25,26], respectively. The robust H 1 control and filtering problems for these systems are also addressed in [27][28][29]. However, given the significance of switched systems analyzed previously and the complexity in dealing with neutrality, only few attempts on stability and control synthesis are made for switched neutral systems [30][31][32]. Moreover, to the best of our knowledge, up to date, no results on the H 1 filter design for switched neutral systems are reported, not to mention the case when the stochastic disturbances and time-varying delays are taken into account.Motivated by the aforementioned discussion, in this paper, we study the problem of rob...

Stability analysis and control for switched stochastic delayed systems

“…The effectiveness of the proposed method is demonstrated by three illustrative examples. STABILITY ANALYSIS AND CONTROL FOR SWITCHED STOCHASTIC DELAYED SYSTEMS 305 of the usage of the non-convolution multiple Lyapunov functionals, the obtained average dwell time is independent of any given decay rate, which generalizes the applicability of the method given in [33]. Second, based on this mean-square exponential stability condition and some stochastic analysis approaches and limit methods in probability, an almost sure exponential stability condition for stochastic switched delayed systems (SSDS) is proposed by avoiding both model transformations (used in [20, 28]) and free matrix variables (used in [21-23]).…”

“…It should be noticed that the average dwell time T A in Proposition 1 can be determined by solving a simple algebraic equation. In contrast with [33], when Proposition 1 is extended to SSDS, we can obtain mean-square exponential stability condition under average dwell time, independent of any given decay rate. If Proposition 1 is applied to delayed systems without stochastic perturbations such as in [10], then the corresponding average dwell time will not depend on any given decay rate.…”

“…Moreover, in Subsection 3.4, we will discuss how to further improve the results when some assumptions are introduced onto the nonlinear stochastic perturbations of SSDS . Remark In Theorem 1, the method of Proposition 1 has been extended to SSDS . It is noticed that the results (including the average dwell time of the switching rule) in depend on the given decay rate α > 0 because of the choice of convolution‐type multiple Lyapunov functionals. The convolution‐type Lyapunov functionals in became non‐convolution ones as those adopted in and in this paper for the case with α = 0.…”

“…It is noticed that the results (including the average dwell time of the switching rule) in depend on the given decay rate α > 0 because of the choice of convolution‐type multiple Lyapunov functionals. The convolution‐type Lyapunov functionals in became non‐convolution ones as those adopted in and in this paper for the case with α = 0. When α = 0, the average dwell time T A = ln( γ / α ) in is meaningless, and the exponential stability under switching signal with the average dwell time for switched systems cannot be ensured .…”

“…The convolution‐type Lyapunov functionals in became non‐convolution ones as those adopted in and in this paper for the case with α = 0. When α = 0, the average dwell time T A = ln( γ / α ) in is meaningless, and the exponential stability under switching signal with the average dwell time for switched systems cannot be ensured . However, like in , non‐convolution Lyapunov functionals is selected herein to obtain the delay‐dependent Theorem 1 for SSDS in this paper.…”