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Almost Asymptotic Regulation of Markovian Jumping Linear Systems in Discrete Time
Author(s) -
He Shuping,
Ding Zhengtao,
Liu Fei
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.828
Subject(s) - exponential stability , mathematics , control theory (sociology) , linear matrix inequality , convex optimization , markov process , discrete time and continuous time , lyapunov function , mathematical optimization , stability (learning theory) , regular polygon , computer science , nonlinear system , control (management) , statistics , physics , geometry , quantum mechanics , machine learning , artificial intelligence
This paper considers the problems of almost asymptotic output regulation for discrete‐time Markovian jumping linear systems. Based on a stochastic Lyapunov‐Krasovskii functional framework, sufficient conditions for the extension of the regulation scheme to such stochastic systems are obtained via state feedback and via error feedback. Relying on a characterization of the feedback controllers, the almost asymptotic regulation is accomplished. The problem of guaranteeing stochastic stability and almost asymptotic tracking is achieved by solving linear matrix inequalities subject to a set of linear equality constraints. In order to ensure relaxed solutions of the regulation equations, a semi‐definite optimization approach via disciplined convex programming is outlined. Simulation results also are given to illustrate the effectiveness of the proposed design approach.

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