Stability analysis of nonlinear time-delay singular systems via improved barbălat’s lemma

Abstract

This paper revisits asymptotic stability problem of nonlinear time-delay singular systems (NTDSs). Many existing stability results for this problem are derived based on the classical Barbălat’s lemma. This lemma puts two requirements on the considered functions or functionals. One is uniform continuity, the other is boundedness of the infinite integral. However, in some cases, the first requirement is difficult to be satisfied. To mitigate this limitation, a novel improved Barbălat’s lemma is proposed in some literature. In this improved lemma, the requirement of uniform continuity is relaxed by quasi-uniform continuity. By virtue of this improved Barbălat’s lemma, this paper establishes a less conservative stability theorem for NTDSs. Then, the derived results related to NTDSs are applied to investigate stability problem of linear time-delay singular systems. To demonstrate the effectiveness of the proposed results, a numerical example about circuit systems is provided.