Improved stability criteria for linear systems with time-varying delays |
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| Institution: | 1. Graduate Program in Electrical Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-010, Brazil;2. Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-010, Brazil;1. School of Automation, China University of Geosciences, Wuhan 430074, China;2. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China |
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| Abstract: | This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods. |
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