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.