Memory state feedback controller design for singular systems with multiple internal constant point delays

The problem of delay-dependent stabilisation for singular linear continuous-time systems with multiple internal incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily tested with numerical or algebraic methods. Based on the Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memory state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free and stable via solving matrix inequality problem. An explicit expression for the desired memory state feedback control law is also given. Finally, a numerical example is presented to illustrate the effectiveness and the availability for the proposed method.