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This paper describes a procedure to solve the global stabilization and tracking problems of the switched nonlinear systems presented in the parametric strict feedback form. In previous studies, simultaneous domination condition (SDC) was introduced for these systems. If this condition is satisfied for all subsystems by means of virtual control laws, a common Lyapunov function (CLF) can be constructed by backstepping approach. As a major drawback of the SDC, this condition cannot be satisfied for complicated switched nonlinear systems. In this paper a new approach based on multiple Lyapunov function (MLF) is introduced which solves the tracking and regulation problems for switched nonlinear systems in strict feedback form without any restriction on the SDC condition. For rendering the merit of the proposed MLF-based backstepping control design, this method is applied practically to a variable structure mechatronic test-bed. According to the simulation and experimental studies, all simple and complicated switched nonlinear systems in strict feedback form can be controlled by the proposed approach.
backstepping; strict feedback; simultaneous domination condition; common Lyapunov function; multiple Lyapunov function; dwell time
Hossein Chehardoli: Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran