h-function-based state bounding results of discrete-time delayed systems

Abstract

This paper focuses on the $h$-function-based state bounding estimation problem for discrete-time nonlinear systems (DTNSs) with time-varying delays and bounded disturbances. First, a direct method based on the system solutions is proposed to provide sufficient conditions, which are composed of simple inequalities and depend on the time delays, to ensure that the state trajectories of the considered system always stay within a polyhedron or converge into it. Second, it is demonstrated that the obtained sufficient conditions are precisely the global $h$-stability (G$h$-S) criteria of the considered system when disturbances disappear, and when the initial function is restricted within a certain range, the resulting polyhedron can be considered as $h$-function-based reachable set estimation of the states. Finally, the applicability of the theoretical results obtained is illustrated through two numerical examples.