Stability and linear quadratic differential games of discrete-time Markovian jump linear systems with state-dependent noise
type: Item
instance of: scholarly article
title: Stability and linear quadratic differential games of discrete-time Markovian jump linear systems with state-dependent noise
zbMATH Open document ID: 1407.49058
DOI: 10.1155/2014/265621
author: Huiying Sun
author: Meng Li
author: Shenglin Ji
author: Long Yan
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 49N70
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 60J20
zbMATH DE Number: 7016028
Wikidata QID: Q59065225
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/265621
OpenAlex ID: W1973707944
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description: scientific article; zbMATH DE number 7016028