Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

This paper investigates the problem of sliding mode control (SMC) for one-sided Lipschitz (OSL) nonlinear Markovian jump systems with partially unknown transition rates. Unmatched norm-bounded uncertainties of state matrices and output matrices are considered. First, a suitable integral-type sliding surface is proposed and a sufficient condition is given such that the sliding mode dynamics is stochastically stable with an <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance level <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula>. Next, an SMC law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, two simulation examples are provided to prove the effectiveness of the proposed approach.

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