Discrete Legendre polynomials-based inequality for stability of time-varying delayed systems |
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| Authors: | Deren Gong Xiaoliang Wang Shufan Wu Xiaodan Zhu |
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| Institution: | 1. School of Aeronautics and Astronautics, Shanghai Jiaotong University, Dongchuan Rd. No. 800, Shanghai 200240, China;2. Chengdu Aircraft Design and research Institute (CADI), Riyue Avenue No.1610, Chengdu 610091, China |
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| Abstract: | This paper proposes Discrete Legendre Polynomial(DLP)-based inequality by solving the best weighted approximation of a given time series. The proposed inequality could significantly reduce the conservativeness in stability analysis of systems with constant or interval time-varying delays. Also former well-known integral inequities, such as discrete Jensen inequality, discrete Wirtinger-based inequality, are both included in the proposed DLP-based inequality as special cases with lower-order approximation. Stability criterion with less conservatism is then developed for both constant and time-varying delayed systems. Several numerical examples are given to demonstrate the effectiveness and benefit of the proposed method. |
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| Keywords: | Corresponding author |
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