Robust sampled-data control of non-linear LPV systems: time-dependent functional approach

This study addresses the problem of robust exponential stability and stabilisation of sampled-data linear parameter varying (LPV) systems with an aperiodic sampling rate. Utilising the input delay approach and taking the distance between real and measured parameters into account, new stability and stabilisation conditions are derived for LPV systems with arbitrary dependence on the parameters. By means of a modified parameter dependent Lyapunov-Krasovskii functional, stability conditions are formulated as a set of parameter-dependent linear matrix inequalities (PLMIs) which are suitable to investigate the effect of 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 a finite number of linear matrix inequalities. Applying the projection lemma new stability analysis conditions are obtained and shown to be suitable for the stabilisation problem. Under the new stability criteria, 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. The proposed method is applied to a sampled-data fuzzy control problem of a non-linear system and multi-rate sampled-data LPV systems. Several examples show the efficiency of the method.