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Zbl 1202.93066
Yang, Hongjiu; Xia, Yuanqing; Shi, Peng
Observer-based sliding mode control for a class of discrete systems via delta operator approach. (English)
[J] J. Franklin Inst. 347, No. 7, 1199-1213 (2010). ISSN 0016-0032; ISSN 1879-2693/e

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 2000:: *93C30 Control systems governed by other functional relations
93D09 Robust stability of control systems
93B07 Observability
93B12 Variable structure systems
93D20 Asymptotic stability of control systems

Keywords: sliding mode observer; sliding mode controller; delta operator system; robust stability; linear matrix inequality (LMI)

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Zentralblatt MATH Berlin [Germany]