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Infinite horizon \(H_\infty\) control for nonlinear stochastic Markov jump systems with \((x, u, v)\)-dependent noise via fuzzy approach. (English) Zbl 1373.93313

Summary: In this paper, the \(H_\infty\) control problem is studied for nonlinear stochastic Markov jump systems with state, control and external disturbance-dependent noise (\((x, u, v)\)-dependent noise for short). A sufficient condition is derived for the infinite horizon \(H_\infty\) control of such systems in terms of a set of coupled second-order Hamilton-Jacobi inequalities (HJIs). In general, it is difficult to solve these coupled HJIs. By using fuzzy approach, the infinite horizon \(H_\infty\) control design for nonlinear stochastic Markov jump systems is developed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Two numerical examples are presented to illustrate the effectiveness of the proposed design methods.

MSC:

93E03 Stochastic systems in control theory (general)
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93C42 Fuzzy control/observation systems
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