Multiple integral inequalities and stability analysis of time delay systems |
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Affiliation: | 1. School of Engineering, Deakin University, Geelong, VIC 3217, Australia;2. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Road, Hanoi, Vietnam |
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Abstract: | This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen’s and Wirtinger’s inequalities, as well as the recently presented Bessel–Legendre inequalities of Seuret and Gouaisbaut (2015) and the Wirtinger-based multiple-integral inequalities of Park et al. (2015) and Lee et al. (2015). The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method. |
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Keywords: | Integral inequalities Stability analysis Continuous-time delay systems Hierarchy of LMIs |
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