Stabilizing switching control for LPV systems with arbitrarily large uncertainty on parameter measures

The purpose of this paper is to define a stabilizing switching policy for LPV systems in the case of physical parameters taking values on a very large set and measured under a possibly unbounded observation noise. No prior knowledge on noise statistics is assumed to be available. A predetermined family F = {G1, …, Gp} of controllers is given, each Gi is properly designed to stabilize the plant on a specific subset of the whole parametric range. The problem considered here consists in defining a supervised switching policy among the elements of F so that the switched closed loop system result to be exponentially stable. The proposed switching logic is based on a suitably defined performance-evaluation criterion based on a Lyapunov-like functional of the output. The exponential stability condition is derived imposing a sufficient long time interval over which the functional is decreasing.