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

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 T n -stability of Markovian jump linear systems wit...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (2014), p.1-11
Main Authors: Yan, Long, Ji, Shenglin, Li, Meng, Sun, Huiying
Format: Article
Language:English
Subjects:
Algorithms
Differential equations
Differential games
Discrete time systems
Economic models
Iterative algorithms
Joining
Linear quadratic
Linear systems
Markov processes
Mathematical analysis
Mathematical models
Mathematical problems
Noise
Optimization
Riccati equation
Stability
Stochastic models
Stochasticity
Studies
Time dependence
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Summary: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 T n -stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic T n -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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/265621