Reachable set estimation for discrete‐time systems with hybrid time‐delays

Abstract

AbstractThis article investigates the problem of reachable set estimation for linear discrete‐time systems (LDSs) with both discrete and distributed delays as well as bounded disturbance inputs. The purpose is to determine a bounded set in which all the LDSs states are in the set. By exploiting Wirtinger‐based summation inequality and linear matrix inequalities techniques, a sufficient criterion is established which guarantees the states of LDSs are bounded by the ellipsoid. An improved Lyapunov–Krasovskii (L‐K) functional is addressed and the L‐K functional matrices are not required all to be positive definite. Finally, the effectiveness and superiority of the proposed methods are substantiated by two numerical examples.