Abstract
In order to achieve more flexibility for state feedback control design, a new design method based on Lipschitz switching surfaces is proposed for a class of n-th order linear systems subject to on-off control input in this paper. The Lipschitz switching surface is piecewise smooth and developed by the combination of several available smooth subsurfaces due to the partitioned domains of interest. Due to the discontinuity of the on-off input, Filippov's differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system. The globally asymptotic stability of the on-off control system with Lipschitz switching surfaces is illustrated by means of nonsmooth analysis and LaSalle's invariant principle for nonsmooth systems.
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