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\(H_\infty\) control of 2-D continuous Markovian jump delayed systems with partially unknown transition probabilities. (English) Zbl 1432.93085
Summary: This study focuses on stochastic stability and \(H_\infty\) control of two-dimensional (2-D) continuous delayed Markovian jump systems (MJSs) with partial information on transition probability. At first, a sufficient condition for the stochastic stability of 2-D MJSs is proposed by choosing an appropriate Lyapunov-Krasovskii functional. Then, the results are developed by designing a state feedback controller that guarantees the stochastic stability of the resultant closed-loop system with a prescribed \(H_\infty\) performance level \(\gamma\). Finally, the proposed results are validated with the help of examples.

MSC:
93B36 \(H^\infty\)-control
93E15 Stochastic stability in control theory
93C43 Delay control/observation systems
60J76 Jump processes on general state spaces
Software:
LMI toolbox
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