Mismatch SMC for Nonlinear Semi-Markovian Jump Models

This paper addresses the mismatch sliding mode control (SMC) for a class of nonlinear semi-Markovian jump models. Under the fact that the modes of original systems are not directly accessible, there exists a detector to estimate values of system modes. Based on these, an suitable sliding surface is designed, in which the SMC mechanism jumps asynchronously with original system. By the key point of stochastic semi-Markovian Lyapunov function, sufficient conditions are established to analysis stochastic stability of sliding mode dynamics. Furthermore, the asynchronous SMC law is designed to force the states of hidden semi-Markovian jump systems onto the predefined switching manifold within a finite time level. Finally, the RLC series circuit illustrates the theoretical findings.