Dynamic Output-Feedback Switching Control for Discrete-Time LPV Switched Systems

This note addresses the problem of robust stabilization of discrete-time switched Linear Parameter-Varying (LPV) systems, where each mode depends on time-varying parameters in a polytope. The aim is to ensure robust stabilization and a bound on the decay rate of the closed-loop trajectories. This is achieved by jointly designing switching rules and fixed-order output feedback controllers by means of Lyapunov-Metzler (LM) inequalities with multiple quadratic Lyapunov functions. The novelty of this work lies on rewriting the LM conditions in an appropriate way that can be solved by an iterative procedure based on linear matrix inequalities. This approach eliminates the need for grid-based procedures, which are commonly used to solve LM inequalities. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed method.