Switched state feedback control for continuous-time polytopic systems and its relationship with LPV control

Abstract

This paper treats switched control design of polytopic systems. Our main goal is to calculate a set of state feedback gains and a switching rule such that the closed loop system remains globally asymptotically stable for all uncertain parameter under consideration, as well as a quadratic on the state guaranteed cost is minimized. The minimum guaranteed cost is assured by choosing, at each instant of time, a feedback gain among a set of previously calculated ones taking into account a multi-objective criterion which allows the closed loop system to present different and possibly conflicting characteristics. The design conditions are based on modified Lyapunov-Metzler inequalities that can be solved by line search coupled to an LMI solver. It is shown that the design technique can be viewed as an alternative to a wide class of LPV control with the clear advantage that the time-varying parameters do not need to be measured online. The theoretical results are illustrated by an academic example consisting of two carts connected by a spring with spring constant modelled as a time-varying uncertain parameter.