On exponential stability of integral delay systems |
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| Authors: | Zhao-Yan Li Bin Zhou Zongli Lin |
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| Affiliation: | 1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China;2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China;3. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743-4743, Charlottesville, VA 22904-4743, USA |
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| Abstract: | This paper is concerned with exponential stability of a class of integral delay systems with a prescribed decay rate. First, by carefully exploring the literature on this topic, a delay decomposition approach is established to reduce the conservatism in the existing sufficient conditions by constructing new Lyapunov–Krasovskii (LK) functionals. It is proven that the proposed sufficient conditions are less conservative than a recently established set of sufficient conditions. Second, by analyzing the characteristic equation of the considered integral delay system, necessary and sufficient conditions for the stability are obtained by computing the right-most zeros of a certain auxiliary point-delay linear system, for which stability criteria that are easy to test are also established based on this method. Numerical examples illustrate the effectiveness of the obtained results. |
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| Keywords: | Integral delay systems Exponential stability Lyapunov&ndash Krasovskii (LK) functional Delay decomposition |
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