Sliding mode control for semi-Markovian jump systems via output feedback

This paper focuses on the output-feedback sliding mode controller design problem for uncertain continuous-time semi-Markovian jump systems (MJSs) in a descriptor system setup. The transition rates (TRs) of semi-MJSs rely on the random sojourn-time, which is different from the constant TRs in the conventional MJSs. By carefully exploiting the dynamical properties of the original system, combining with the switching functions, a descriptor system is firstly formulated to describe the holonomic dynamics of the sliding mode. Then, with the construction of a semi-Markovian Lyapunov function and the full utilization of the characteristics of cumulative distribution functions, a sufficient condition on the sliding surface synthesis is presented, which also guarantees the stochastic stability (SS) of sliding mode dynamical system. Furthermore, a sliding mode controller is synthesized to drive the underlying closed-loop system onto the sliding surface in finite time, locally for a given sliding region. Finally, an illustrative example is carried out to validate the effectiveness of the developed approach.