Stabilization of two kinds of nonhomogeneous Markovian jump systems via sliding mode control

In this article, the stabilization is addressed for the continuous-time nonhomogeneous nonlinear Markovian jump system (MJS) with parameter uncertainty and stochastic disturbance via sliding mode control (SMC) technique. By using a piecewise homogeneous Markov chain to describe its time-varying characteristics, the considered nonhomogeneous MJS is established by two kinds of piecewise homogeneous MJSs. After that, an integral sliding mode function is constructed. Then, by applying the SMC theory, two control schemes are proposed to force the states of the piecewise homogeneous MJSs onto the designed sliding surface. Sufficient conditions are given to assure the stochastic stability of the sliding mode dynamics. In addition, the reachability of the system states under the developed SMC law is discussed via Lyapunov stability theory. Lastly, some simulation results are provided to show the effectiveness of the presented SMC methods.