Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities

Author

Mahmoud, Magdi S. ; Shi, Peng

Author_Institution

Fac. of Eng., Arab Acad. for Sci. & Technol., Helliopolis-Cairo, Egypt

Volume

49

Issue

4

fYear

2002

fDate

4/1/2002 12:00:00 AM

Firstpage

538

Lastpage

542

Abstract

In this work, we investigate the H_∞ control problem for a class of linear discrete-time systems with Markovian jump parameters. The jump parameters considered here are modeled by a discrete-time Markov process. Our attention is focused on the design of a state feedback controller such that both stochastic stability and a prescribed H_∞ performance are required to be achieved when the real system under consideration is affected by both unknown nonlinearity and norm-bounded real time-varying uncertainties. Sufficient conditions are proposed to solve the above problem, which are in terms of a set of solutions of linear matrix inequalities (LMIs)

Keywords

H^∞ control; Markov processes; closed loop systems; control system synthesis; discrete time systems; linear systems; matrix algebra; nonlinear control systems; robust control; state feedback; H_∞ control problem; LMI; Markovian jump linear discrete-time systems; Markovian jump parameters; Riccati-like inequalities; linear matrix inequalities; nonlinear discrete-time systems; norm-bounded uncertainties; prescribed H_∞ performance; real time-varying uncertainties; robust control; state feedback controller design; stochastic stability; unknown nonlinearity; Control systems; Markov processes; Nonlinear control systems; Robust control; Stability; State feedback; Stochastic systems; Sufficient conditions; Time varying systems; Uncertainty;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.995674

Filename

995674