Stabilizing backstepping controller design for arbitrarily switched complex nonlinear system

Abstract In this paper, the aim is to design a backstepping controller for switched complex nonlinear system. The nonlinear system is composed of several arbitrarily switched complex nonlinear subsystems, and the nonlinear system does not satisfy the so-called hypothesis of the global Lipschitz-like condition. First an uniform nonlinear decoupling method for switched subsystems is proposed to overcome the double uncertainty from the complex nonlinear structure and arbitrarily switching. Next a states backstepping controller is designed to realize exponentially stability of the switched nonlinear systems. Then based on an uniform gain observer with the uncertainty of the subsystem nonlinearity, an output backstepping controller is construct to realize exponentially stability of the observer-backstepping feedback control system. Two detailed simulations are finally presented to exhibit the effectiveness of the proposed synthesis methods.

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