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		Jiangyan ZHANG,Tielong SHEN.[en_title][J].Control Theory and Technology,2013,11(2):268~274.[Copy]

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JiangyanZHANG,TielongSHEN
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(Department of Engineering and Applied Sciences, Sophia University; College of Electromechanical & Information Engineering, Dalian Nationalities University)

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Received:December 25, 2011Revised:April 26, 2012

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Feedback stabilization for a class of discontinuous systems driven by integrator

Jiangyan ZHANG,Tielong SHEN

(Department of Engineering and Applied Sciences, Sophia University; College of Electromechanical & Information Engineering, Dalian Nationalities University)

Abstract:

This paper investigates the feedback stabilization problem for a class of discontinuous systems which is characterized by Filippov differential inclusion. Lyapunov-based backstepping design method is generalized with nonsmooth Lyapunov functions to solve the control problem. A set-valued time derivative is introduced first for nonsmooth function along discontinuous vector fields, which enables us to perform Lyapunov-based design with nondifferentiable Lyapunov function. Conditions for designing a virtual control law which is shown nondifferentiable in general in the recursive design problem are proposed. Finally, as a special case, piecewise linear system is discussed to demonstrate the application of the presented design approach.

Key words: Differential inclusion Discontinuous systems Backstepping Nonsmooth Lyapunov function