A numerical optimization approach to switching surface design for switching LPV control

This paper proposes an algorithm to design switching surfaces for the switching linear parameter-varying (LPV) controller with hysteresis switching. The switching surfaces are sought for to optimize the bound of the closed-loop L₂-gain performance. An optimization problem is formulated with respect to parameters characterizing Lyapunov matrix variables, local controller matrix variables, and locations of the switching surfaces. Since the problem turns out to be non-convex in terms of these characterizing parameters, a numerical algorithm is given to guarantee the decrease of the cost function value after each iteration. A hybrid method which combines the steepest descent method and Newton´s method is employed in each iteration to decide the update direction of switching surface parameters. A simple numerical example is provided to demonstrate the validity of the proposed algorithm.