The Stability Analysis Of Linear Time-delay Systems Based On Delay Decomposition Approach

Nowadays, time-delay exists in almost all control systems. Due to the time-delay, the controlsystem may be unstable, even its performance deteriorated. It also brings a lot of difficulties to thetheoretical analysis and design of engineering. Therefore, in order to optimize system’sperformance, the stability of time-delay systems must be studied at the first place. The study oftime-delay systems becomes a hot issue in the field of control and how to make stability better alsobecomes a focus problem for a lot of domestic and foreign scientists.In recent years, the stability of system has been deeply studied. Based on the analysis of aserial of domestic and foreign literatures, the stability of linear delay systems has been studied usingdelay decomposition approach by choosing appropriate Lyapunov-Krasovskii functionals in thispaper. The results were given by the means of LMIs, which are easy to be solved.This article is composed by the following aspects:1. First, the background and significance of linear time-delay systems are described and theresearch status of time-delay problems by domestic and foreign scholars is reviewed. Then, theresearch methods about the stability of the time-delay systems are summarized, the given examplesillustrate the phenomenon that time-delay systems exist in all kinds of actual system, and thecontent of this article is simply presented. At last, preliminary knowledge and some common lemmaare introduced.2. As to linear systems with constant time delay, two stability criteria proposed by Gouaisbautand Han which based on delay decomposition approach are compared. The relationship between thetwo approaches is strictly established theoretically, and the advantages and disadvantages of themare analyzed by computational complexity and numerical examples.3. As to linear systems with interval fast time-varying delay, two new stability criterions useddelay decomposition approach are given. Lower bound and upper bound of time-delay are dividedinto two subintervals. Then, two better stability criterions are given by using convex combinationprinciple. The advantages and disadvantages of the four stability criterions are compared bynumerical examples, simulation and computational complexity.4. As to linear systems with interval slow time-varying delay, two new stability criterions useddelay decomposition approach are given. The method makes full use of the information of lowerbound, upper bound and rate of time delay change which are divided into two subintervals. Somenumerical examples have been provided to illustrate the improvement of the proposed results.5. The content of the paper are summarized, and the problems which are unsolved or need to be improved are described.