H_∞ performance for neutral-type Markovian switching systems with general uncertain transition rates via sliding mode control method

The paper is devoted to the investigation of observer-based H_∞ sliding mode controller design for a class of nonlinear uncertain neutral Markovian switching systems (NUNMSSs) with general uncertain transition rates. In this case, each transition rate can be completely unknown or only its estimate value is known. Firstly, an H_∞ non-fragile observer subjected to the general uncertain transition rates of the NUNMSSs is constructed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are founded. Secondly, the state-estimation-based sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval. Thirdly, an asymptotically stochastic stability criterion is established by utilizing a new-type Lyapunov function to 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.