Abstract

This paper addresses the problem of robust exponential stability and stabilisation of sampled-data linear parameter varying (LPV) systems with aperiodic sampling rate. The main contribution of this paper is the derivation of new stability and stabilisation conditions for sampled-data LPV systems with arbitrary dependence on the parameters with taking into account the distance between real and measured parameters. The proposed method utilises the input delay approach based on a modified parameter and time dependent Lyapunov-Krasovskii functional (LKF) and provides stability conditions. The stability conditions are formulated as a set of parameter-dependent linear matrix inequalities (PLMIs) which are suitable to investigate the effect of the parameters variation rate and the sampling rate on the closed-loop stability. Furthermore, sufficient conditions to guarantee the feasibility of PLMIs over the set of whole parameters are derived that lead to the feasibility of finite number of linear matrix inequalities (LMIs). Thereafter, using projection Lemma new stability analysis conditions are obtained and shown to be suitable for the stabilisation problem. Utilising the proposed stability analysis conditions an efficient procedure developed for robust sampled data controller design in the presence of uncertainty on the varying parameters and unknown time varying sampling rate. Proposed method is applied to sampled-data fuzzy control problem of nonlinear system and multi-rate sampled-data LPV systems. Several examples show the efficiency of the method.