Equivalence of stability criteria for time-delay systems

Abstract

During the past few decades, there have been a number of new delay-dependent stability criteria based on linear matrix inequalities published in the literature. These criteria, to some extent, can reduce the conservativeness. In fact, some criteria are equivalence. In this paper, we aim to theoretically establish equivalence of two stability criteria. One was obtained by Sun et al. [Sun et al. In: Proceedings of IEEE Power & Energy Society General Meeting. 2009, 1–7] and the other was given by Xu et al. [Xu et al. IEEE Transactions on Automatic Control, 2005, 50(3): 384–387]. Also, we theoretically establish equivalence of the robust stability criterion presented by Jia et al. [Jia et al. Automation of Electric Power Systems, 2010, 34(3): 6–11] and the one given by Xu et al. (2005).

Key words： delay-dependent stability criterion; robust stability; time-delay systems; linear matrix inequality (LMI)