Adaptive quantised H_∞ observer-based output feedback control for non-linear systems with input and output quantisation

This study investigates the case of simultaneous input and output quantisation for a class of non-linear output feedback systems subject to uncertain non-linear dynamics and non-zero initial states. An adaptive quantised observer-based output feedback controller is designed to guarantee bounded stability and H_∞ performance despite input and output quantisation. In comparison with the existing work, the main contributions of this study are that: (i) an important lemma is proposed to remove the matrix equality constraint used in many existing results, and three new design methods in strict terms of linear matrix inequality techniques are proposed; (ii) this study focuses on eliminating the impact of both input and output quantisation errors. Since the impact of input and output quantisation errors cannot be fully eliminated, the estimation error is proved to be ultimately bounded and to converge to a residual set; and (iii) an adaptive compensation term is constructed to compensate for the time-variant effects caused by non-linear dynamics and uncertain parameter vectors. Finally, two numerical examples are given to show the efficacy and advantages of the proposed methods.