Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Huiying Sun,Shenglin Ji,Long Yan,Meng Li

doi:10.1155/2014/265621

Abstract

We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ) differential games. A necessary and sufficient condition involved with the connection between stochasticTn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochasticTn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs). Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

Highlights

In this paper we discuss linear systems with Markovian jump and state-dependent noise
In [25], we have considered linear quadratic (LQ) differential games in finite horizon for discrete-time stochastic systems with Markovian jump parameters and multiplicative noise
On the basis of [26], in the paper we further investigate the LQ differential games for discretetime MJSLS with a finite number of jump times

Summary

Introduction

In this paper we discuss linear systems with Markovian jump and state-dependent noise. In [24], we have considered stochastic differential games in infinite-time horizon.

Results

Conclusion