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In this paper, we concern the approaching condition of sliding mode control (SMC) with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov’s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov’s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output (SISO) systems, of which the switching surface is designed Lips chitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.
In this paper, we concern the approaching condition of sliding mode control (SMC) with a Lipschitz switching surface that may be nonsmooth. Filippov’s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov’s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output (SISO) systems, of which the switching surface is designed Lips chitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.