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Optimal switching surface design for state-feedback switching LPV control

In this paper, we deal with the problem of simultaneous design of state-feedback switching linear parameter-varying (LPV) controllers and switching surfaces for LPV plants to further improve the performance of the switching LPV controllers. The LPV plants that we consider have polynomially parameter-dependent state-space matrices. Using slack variable approach, we first propose a method to design state-feedback switching LPV controllers, and then formulate simultaneous design problem as an optimization problem involving bilinear matrix inequalities (BMIs). An algorithm is then proposed to solve the problem by iteratively fixing either switching surface variables or controller variables while optimizing the other. A simple numerical example is given to demonstrate the effectiveness of the proposed approach.