A sliding mode approach to H_∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems

This paper is focused on designing an H_∞ sliding-mode control for a class of neutral-type stochastic systems with Markovian switching parameters and nonlinear uncertainties. An H_∞ non-fragile observer subjected to the transition rates of the switching mode is firstly constructed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are established. Then, the state-estimation-based sliding mode control law is designed to guarantee the reachability of the sliding surface in finite time interval. Furthermore, a stochastic stability criterion is established for all admissible uncertainties, which can guarantee the error system and sliding mode dynamics to be asymptotically stochastic stable with a given disturbance attenuation level. Finally, an example is provided to illustrate the efficiency of the proposed method.