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

This 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.