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

Dong-Hoon Lee, Yeong-Jae Kim, Seung-Hoon Lee and Oh-Min Kwon ()
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Dong-Hoon Lee: Korea Water Resources Corporation (K-Water), Daejeon 34045, Republic of Korea
Yeong-Jae Kim: School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea
Seung-Hoon Lee: Division of Electrical and Electronics Engineering, Korea Maritime and Ocean University, Busan 49112, Republic of Korea
Oh-Min Kwon: School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea

Mathematics, 2024, vol. 12, issue 14, 1-19

Abstract: This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, the compositions of the LKFs are considered to enhance the feasible region of the 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. 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 four examples. Four numerical examples show that the proposed Theorems 1 and 2 obtain less conservative results than existing outcomes. Particularly, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1 in some specific systems.

Keywords: augmented approaches; linear system; Lyapunov–Krasovskii functional; stability analysis; time delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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