H∞ control of 2-D continuous Markovian jump delayed systems with partially unknown transition probabilities

Abstract This study focuses on stochastic stability and H∞ 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∞ performance level γ. Finally, the proposed results are validated with the help of examples.

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