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H ∞ ‐type control for discrete‐time stochastic systems
Author(s) -
El Bouhtouri A.,
Hinrichsen D.,
Pritchard A. J.
Publication year - 1999
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199911)9:13<923::aid-rnc444>3.0.co;2-2
Subject(s) - type (biology) , discrete time and continuous time , control (management) , computer science , control theory (sociology) , mathematics , statistics , artificial intelligence , geology , paleontology
In this paper we consider discrete‐time, linear stochastic systems with random state and input matrices which are subjected to stochastic disturbances and controlled by dynamic output feedback. The aim is to develop an H ∞ ‐type theory for such systems. For this class of systems a stochastic bounded real lemma is derived which provides the basis for a linear matrix inequality (LMI) approach similar to, but more general than the one presented in Reference 1 for stochastic differential systems. Necessary and sufficient conditions are derived for the existence of a stabilizing controller which reduces the norm of the closed‐loop perturbation operator to a level below a given threshold γ . These conditions take the form of coupled nonlinear matrix inequalities. In the absence of the stochastic terms they get reduced to the linear matrix inequalities of deterministic H ∞ ‐theory for discrete time systems. Copyright © 1999 John Wiley & Sons, Ltd.