Relaxed results on reachable set estimation of singular system with time-varying delay

This paper further investigates the problem of reachable set estimation (RSE) for a class of continuous-time singular systems with time-varying delay. First, we use the relaxed Lyapunov–Krasovskii functional to tackle the RSE problem. This functional does not need all the matrices concerned to be positive definite. In addition, a novel weighted integral inequality and time-delay partition approach are utilized to reduce conservatism in the results. Based on these methods, sufficient conditions in the form of linear matrix inequalities are established. Finally, the correctness and validity of these relaxed results are demonstrated by three simulation examples.