Delayed Decomposition Approach to Delay-Dependent Stability for Time-Varying Delay Descriptor Systems

Abstract

This paper studies the problem of stability analysis for descriptor systems with time-varying delay. By developing a delayed decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay- dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. It is proved that the newly proposed criteria may introduce less conservatism than some existing ones. Meanwhile, the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.