New results on state bounding for discrete‐time systems with interval time‐varying delay and bounded disturbance inputs

Abstract

This study considers the problem of state bounding for a class of discrete-time systems with interval time-varying delay and bounded disturbance inputs. By using an improved Lyapunov–Krasovskii functional combining with the delay-decomposition technique and the reciprocally convex approach, the authors first derive new delay-dependent conditions in terms of matrix inequalities to guarantee the existence of a ball such that, for any initial condition, the state trajectory of the system is either bounded within that ball or converges exponentially within it. On the basis of these new conditions, the authors then derive an improved ellipsoid reachable set bounding and a new result on exponential stability of discrete-time systems with interval time-varying delay. Numerical examples are presented to show the effectiveness of the obtained results and improvement over existing results.