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Robust stabilization of non-minimum phase switched nonlinear systems with uncertainty. (English) Zbl 1447.93295

Summary: This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase. The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics. Then, a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms. Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem, which guarantees the global asymptotical stability of the resulting switched system. Obviously, the proposed control approach can improve more the transient state, compared to a feedback linearization based on only one diffeomorphism. Simulation studies illustrate the effectiveness of the suggested approach.

MSC:

93D21 Adaptive or robust stabilization
93D23 Exponential stability
93B12 Variable structure systems
93C41 Control/observation systems with incomplete information
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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