Direct discrete-time design approach to robust sampled-data observer-based output-feedback fuzzy control

Abstract

This paper addresses a direct discrete-time design methodology for a robust sampled-data observer-based output-feedback stabilisation problem for a class of non-linear systems suffering from parametric uncertainties and disturbances that is identically modelled as a Takagi–Sugeno (T–S) fuzzy model at least locally. The primary features in the current development are that (1) we are based on an exact (rather than approximate) discrete-time model in an integral (rather than closed) form while (2) the control performance is characterised with respect to an (rather than l2) norm. It is shown that the uncertain sampled-data non-linear control system is robustly asymptotically stable if the employed discrete-time model is so. Design conditions are investigated in the discrete-time Lyapunov sense and concretised in the format of linear matrix inequalities.