Robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control

This study deals with the problem of robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control (SMC). Such a switching is governed by a semi-Markovian process which is time-varying and dependent on the sojourn-time h. The time delay is considered as time-varying and meets the requirements of the upper and lower bounds. By introducing free-connection weighting matrix method and Lyapunov functional, sufficient conditions for the resulting sliding mode dynamics in the form of linear matrix inequalities are derived to guarantee the closed-loop system robustly stochastically stable for all admissible uncertainties and non-linear perturbations. Then, an SMC law is synthesised to drive the system trajectories onto the predefined switching surface in a finite time. Finally, an example illustrates the validity of the obtained results.