A delay fractioning approach to robust sliding mode control for discrete-time stochastic systems with randomly occurring non-linearities. (English) Zbl 1228.93025

Summary: In this paper, the robust Sliding Mode Control (SMC) problem is investigated for a class of uncertain discrete-time stochastic systems with randomly occurring non-linearities and time delays. The randomly occurring non-linearity, which describes the phenomena of a class of non-linear disturbances occurring in a random way, is modelled according to a Bernoulli distributed white sequence with a known conditional probability. By constructing a novel Lyapunov-Krasovskii functional, the idea of delay fractioning is applied to cope with the robust SMC problem with time delays. Sufficient conditions are derived to ensure the stability of the systems dynamics in the specified sliding surface. Such conditions are characterized in terms of a set of linear matrix inequalities with an equality constraint. A discrete-time SMC law is synthesized to guarantee the reaching condition of the discrete-time sliding mode surface. Finally, a simulation example is presented to illustrate the effectiveness of the proposed results.


93B12 Variable structure systems
93B35 Sensitivity (robustness)
93C55 Discrete-time control/observation systems
93E03 Stochastic systems in control theory (general)
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