Dissipative controller design for uncertain neutral systems with semi‐Markovian jumping parameters

Abstract

Summary This paper is concerned with the problem of dissipative controller design for neutral systems with semi‐Markovian jumping parameters and norm‐bounded parameter uncertainties. First, a new stability criterion is obtained by applying a more accurate integral inequality and a delay‐partitioning approach, which is less conservative than those existing results. Second, based on the stability criterion, sufficient conditions for the existence of a state‐feedback controller, which ensures that the resulting closed‐loop system is stochastically stable and dissipative, are proposed. The controller gains can be obtained by using feasible solutions to a certain set of linear matrix inequalities. Finally, 2 numerical examples are provided to illustrate the effectiveness of the controller design method.

Event-Triggered Dissipative Filter Design for Semi-Markovian Jump Systems with Time-Varying Delays

“…In this section, we carry out the analysis of stochastic stability and dissipativity for the resulting filtering error system (9). en, on the basis of these results, the desired filter design scheme for system (1) is established.…”

“…Definition 2 (see [9,43]). For given matrices Z, Y, X with Z ≤ 0 and X is symmetric, the filtering error system (9) is said to be dissipative, if there exist θ > 0, such that for any T > 0 and zero initial condition, the following inequality holds:…”

“…To mention a few, the problem of stability and stabilization for semi-Markovian jump systems was addressed in [5][6][7]. e controller design problem for semi-Markovian jump systems was investigated in [8][9][10][11]. In [12,13], the filtering problem for semi-Markovian jump systems was considered.…”

Stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters via novel free matrix–based integral inequality

“…The reliable mixed passive and H ∞ filtering problem has been studied for uncertain semi‐Markov jump delayed systems subject to sensor failures in the work of Shen et al The sliding‐mode controller design problem has been discussed for semi‐Markovian jump systems in the work of Chen et al An H ∞ state‐feedback controller has been designed in the work of Huang et al to solve the active fault‐tolerant control problem of semi‐Markovian jump systems. The problem of nonfragile finite‐time L 2 − L ∞ state estimation for discrete‐time neural networks with semi‐Markovian switching has been considered in the work of Rakkiyappan et al Very recently, the problem of ‐dissipativity controller design for neutral systems with semi‐Markovian jumping parameters and norm‐bounded parameter uncertainties has been considered in the work of Xia et al via applying a more accurate integral inequality and delay‐partitioning approach. However, as mentioned in the work of Zhang et al, the L 2 − L ∞ performance is not contained in dissipativity, and a more general performance called extended dissipativity is established to unify the dissipativity and L 2 − L ∞ performance for Markovian jumping systems.…”

“…Therefore, to relax this assumption, the concept of a semi-Markov chain, where the transition probabilities are time varying and dependent on the sojourn time, has been introduced in the work of Huang and Shi. 40 Some significant results of semi-Markovian jumping systems have been published in the literature, [41][42][43][44][45][46][47][48][49][50] for example, the problem of stability and stabilization for a class of discrete-time semi-Markov jump systems has been investigated in the work of Zhang et al 41 by the semi-Markov kernel approach. In the work of Li et al, 42 the sliding-mode control problem for the phase-type semi-Markovian jump system has been solved by using a supplementary variable technique and plant transformation.…”