Sampled-data LPV Control: a Looped Functional Approach

Abstract

This paper addresses the problem of stability and stabilization of sampled-data linear parameter varying (LPV) control systems. It is explicitly assumed that the LPV-controller is updated only at the sampling instants and that the control signal is kept constant between two consecutive samples by means of a zero order holder, while the plant and the scheduling parameter evolve continuously in time. In this case, conditions that allow to compute a sampled-data LPV state feedback control law that ensures the asymptotic stability of the closed-loop system, provided that the intersampling interval respect some bounds, are proposed in a quasi Linear Matrix Inequality (LMI) form (i.e. they are LMIs provided a scalar parameter is fixed). The approach is based on a polytopic modeling of the LPV system and the use of a parameter dependent looped-functional to take into account the sampling effects. Both periodic and aperiodic sampling cases can be handled. A numerical example illustrates the application of the proposed methodology.