Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via Augmented Lyapunov-Krasovskii functional

• DOI: 10.20944/preprints202405.1952.v1
• Publication Date: 2024-05-30T05:18:32Z
• Authors: Dong-Hoon Lee; Yeong-Jae Kim; Seung-Hoon Lee; Oh-Min Kwon
• Keywords: QA1-939; Lyapunov–Krasovskii functional; linear system; stability analysis; time delay; Mathematics; augmented approaches

This work investigates the stability conditions for linear systems with time-varying delays via augmented Lyapunov-Krasovskii functional(LKF). Two types of augmented LKFs with cross terms in integral are suggested to improve the stability conditions for interval time-varying linear systems. Through this work, the compositions of the LKFs are considered to enhance the feasible region of stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality(WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality(LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. And then simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in two examples. Two numerical examples show that the proposed Theorem 1 and 2 obtained less conservative results than existing outcomes. Also, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1’s in some specific systems.