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Control design of a class of linear systems based on combined nonsmooth switching surfaces

In order to improve flexibility of control design for a class of n-th order linear systems with on-off control input, a new method based on combined nonsmooth switching surfaces is proposed in this paper. The combined switching surface is piecewise smooth and developed by the combination of several available smooth subsurfaces due to the partitioned domains of interest. Filippov's differential inclusion is adopted to describe the dynamics of the closed-loop system due to the discontinuity of the on-off input. The globally asymptotic stability of the closed-loop system is illustrated in the framework of nonsmooth analysis, and the effectiveness of the method is demonstrated by a numerical simulation.