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

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  • Huiying Sun
  • Meng Li
  • Shenglin Ji
  • Long Yan

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 stochastic -stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic -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.

Suggested Citation

  • Huiying Sun & Meng Li & Shenglin Ji & Long Yan, 2014. "Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, November.
    • Handle: RePEc:hin:jnlmpe:265621
    DOI: 10.1155/2014/265621
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