Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems. Issue 17 (November 2020)

• Record Type: Journal Article
• Authors: Wang, Hui; Xu, Huiling; Zhai, Xiaokai; Chen, Xuefeng; Lin, Zhiping
• Is Part Of: Journal of the Franklin Institute. Volume 357:Issue 17(2020)
• Page Start: 12670
• Page End: 12699
• Publication Date: 2020-11
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2020.08.038
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper deals with problems of asymptotic stability analysis and model reduction for spatially interconnected continuous time-delay systems. The well-posedness, asymptotic stability, and contractiveness of spatially interconnected continuous-time state-delay systems are appropriately defined. The Lyapunov–Krasovskii method is extended for asymptotic stability analysis of spatially interconnected continuous time-delay systems in infinite-dimensional space. A sufficient condition based on the given system matrices is presented in terms of linear matrix inequalities to check the well-posedness, asymptotic stability, and contractiveness. We then obtain a sufficient condition for the existence of a delay-free reduced-order system for a given spatially interconnected continuous time-delay system. Employing the elimination lemma and the cone complementary linearization algorithm, we can obtain a delay-free reduced-order system. Finally, two examples are used to demonstrate the effectiveness and applicability of the proposed method.