Dissipative Filtering of Markovian Jumping Systems via Adaptive Sliding Mode Control

In this study, dissipative filtering of Markovian jumping systems (MJSs) is investigated using the sliding mode control (SMC) method. A novel dynamic model considering linearity and nonlinearity was proposed, and an adaptive sliding motion controller was established to study the dissipation and mean-square exponential stability. First, MJSs with time-varying delays are proposed, which involve known and unknown nonlinear functions. Subsequently, a novel sliding mode surface (SMS) function was constructed to ensure that the trajectory of the sliding motion dynamics could move along the SMS. In addition, an appropriate SMC rule was presented to guarantee SMS accessibility. Second, the filter was obtained through dissipation theory, which ensures that the filtering error system is extended-dissipative and the mean-square is exponentially stable. Finally, the effectiveness of this method was verified using a practical example.