Integrator-based robust ℋ_∞ sliding mode control of uncertain stochastic Markovian jump delay systems with non-linear perturbations

This study is concerned with the problem of robust ℋ_∞ sliding mode control (SMC) of It ô stochastic delayed Markovian jump systems subject to parameter uncertainties and non-linear perturbations. Firstly, for the sake of practicality, a common integral sliding surface functional without time-varying delay is proposed. Then, by using linear matrix inequalities technique, sufficient condition for the robust mean-square exponential stability of the resulting closed-loop system with a prescribed disturbance attenuation level γ is derived. Moreover, a novel sliding mode controller is designed such that system trajectories can be kept on the sliding surface almost surely since the initial time. Finally, an example is provided to illustrate the effectiveness of the obtained result.