Reachable Set Estimation for Singular Discrete-Time Nonlinear Systems With Time-Varying Delays

Abstract

In this article, the reachable set estimation problems for a class of singular discrete-time nonlinear systems (SDNS) with time-varying delay (TVD) are presented. First, we employ a Lyapunov function scheme and utilize zero-type free matrix equations. Based on this, a criterion is derived in the form of linear matrix inequalities (LMIs) to guarantee that the considered system to be regular, causal, and the state trajectory $x_1$ of the system is bounded. Second, by developing the singular systems decomposition technique into slow and fast subsystems and using the introduced auxiliary lemma, we establish that the $x_2$ state trajectory of the fast subsystem is also bounded, and the reachable set of singular nonlinear system is bounded within the ellipsoid. Finally, Numerical examples are presented to illustrate the effectiveness of the proposed method.