Abstract
This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities (LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.
Highlights
Markovian jump systems have been widely investigated as a kind of special and important hybrid dynamic systems (HDS) [1]
When abrupt changes of the matrix parameters of systems are governed by a Markov chain, it is natural to be modeled as Markovian jump systems
Motivated by the aforementioned discussion, in this paper, we study the stochastic stabilization of discrete-time Markovian jump systems (MJSs) with time-varying delay and two Markov chains under partly known transition probabilities
Summary
Markovian jump systems have been widely investigated as a kind of special and important hybrid dynamic systems (HDS) [1]. Y. Li et al.: Stochastic Stabilization for Discrete-Time MJSs With Time-Varying Delay and Two Markov Chains discussed in [10]–[13], such as filter design, fault detection and guaranteed cost control. In [16], by feedback controls based on discretetime state observations, the robust stabilization is studied for continuous-time hybrid stochastic systems with time-varying delay. Motivated by the aforementioned discussion, in this paper, we study the stochastic stabilization of discrete-time MJSs with time-varying delay and two Markov chains under partly known transition probabilities. We study the design of the state feedback controller for discrete-time MJSs with time-varying delay and partly known transition probabilities, where the mode switches are governed by two independent Markov processes.
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