Reliable l2–l∞ and H∞ Control for Nonlinear Singular Systems via Dynamic Output Feedback

Abstract

The reliable $l_2\text{–}{l}_{\mathrm{\infty }}$ and $H_{\mathrm{\infty }}$ control for a class of Lipschitz nonlinear discrete-time singular systems with time delay is investigated via dynamic feedback control. The main goal of this paper is to design a generalized nonlinear controller such that, for possible actuator failures, the closed-loop system is regular, casual, and stable with a given $l_2\text{–}{l}_{\mathrm{\infty }}$ and $H_{\mathrm{\infty }}$ disturbance attenuation level being satisfied. Some sufficient conditions are obtained in terms of linear matrix inequalities (LMIs), and the controller design method is also proposed. Finally, a numerical example is included to illustrate the effectiveness of our proposed results.