Robust finite‐time H_∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

Abstract

In this article, the problem of robust finite-time H ∞ synchronization control is investigated for a class of uncertain discrete-time master-slave systems with Markovian switching parameters in the observer-based case. Parameter uncertainties are assumed to be norm-bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain.By using stochastic Lyapunov function method and finite-time analysis techniques, novel sufficient conditions that include the master-slave parameters are obtained for designing an observer-based finite-time H ∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations. K E Y W O R D Sfinite-time control, nonhomogeneous Markovian jump systems, observer-based control, parameter uncertainties, synchronization INTRODUCTIONMarkovian jump systems (MJSs), as a class of stochastic hybrid systems, have received a great deal of interest due to their effectiveness of modeling dynamic systems with random abrupt changes on structures and parameters. What characters these systems is that the system modes evolve subject to a Markov chain, which follows its own transition probabilities (TPs). Much attention has been devoted to the research to obtain more appropriate assumptions on TPs, 1-5 for the reason that traditionally ideal assumption on TPs limits the applicability of the relevant results. Significantly, the Markov chains in most of the aforementioned works are assumed to be homogeneous, 6-8 namely, the TPs are time-invariant. In reality, however, the switching of system mode is usually affected by multiple factors at the same time, and each factor may have different degree of influence on it at different times. For example, Markov chain can be an effective tool to describe networked delays, 9,10 and the variation rate of delays is affected by various factors at different times, such as poor quality of communication lines, network-loaded servers, and so on. Apparently, during the period of system operating, the network congestion and the condition of communication facilities are "persistently" varying. This phenomenon leads to the research of nonhomogeneous Markov chain, in which the transition probabilities are time-varying. In the existing control literature studies, the character of time-varying TPs is mainly divided into two categories: finite piecewise homogeneous and polyhedral. It is noteworthy that the finite piecewise homogeneous type of time-varying TPs is only a special case of polyhedral time-varying TPs. To investigate nonhomogeneous MJSs with polyhedral time-varying TPs, related works have been reported in recent years. The problem of stochastic stabilization for nonhomogeneous MJSs was first investigated in Reference 11. References 12 and 13 studied the problems of H ∞ control and output feedback control for nonhomogeneous 3982

Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities

“…According to the proof of Theorem 2, it is obvious that condition (36) will be guaranteed by (39) to (41). Remark 6.…”

“…In addition, by solving LMIs (37), ( 39), ( 40), (41) ,and (44), we have σ 2 = 0.1779, ϱ 1 = 0.9901, and ϱ 2 = 5.2268, and the gains of observer-based state feedback controller (32) are as follows: The trajectories of system state η(k) for CLS (33) and the curve of the control input u(k) of ( 32) are illustrated in Figure 11. Moreover, Figure 12 shows the trajectories of η T (k) R i η(k) (50 curves) and E{η T (k) R i η(k)} of closed-loop system (33).…”

“…To weaken the effect of external disturbances, H ∞ control has emerged. Recently, many scholars have carried out plenty of research on finite-time H ∞ control [35][36][37][38][39][40][41]. Specifically, ref.…”

“…On the other hand, due to the constraints of measurement technology and measurement costs, the system state information is frequently challenging to measure directly. In tackling this challenge, many meaningful results of finite-time H ∞ observer-based controller designing schemes have been successfully attained; see [37][38][39][40][41] and references therein.…”