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Observer-based sliding mode control for a class of discrete systems via delta operator approach. (English) Zbl 1202.93066

Summary: In this paper, an observer-based Sliding Mode Control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.

MSC:

93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93D09 Robust stability
93B07 Observability
93B12 Variable structure systems
93D20 Asymptotic stability in control theory
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