New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities |
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| Authors: | Reza Mohajerpoor Lakshmanan Shanmugam Hamid Abdi Rajan Rakkiyappan Saeid Nahavandi Peng Shi |
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| Affiliation: | 1. Institute of Transport Studies, Department of Civil Engineering, Monash University, Melbourne, VIC, Australia;2. School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, 5005 SA, Australia;3. Research Center for Wind Energy Systems, Kunsan National University, Kunsan, Republic of Korea;4. Institute for Intelligent Systems Research and Innovation, Deakin University, Geelong, VIC, Australia;5. Department of Mathematics, Bharathiar University, Coimbatore, India |
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| Abstract: | Stability conditions for time‐delay systems using the Lyapunov‐based methodologies are generically expressed in terms of linear matrix inequalities. However, due to assuming restrictive conditions in deriving the linear matrix inequalities, the established stability conditions can be strictly conservative. This paper attempts to relax this problem for linear systems with interval time‐varying delays. A double‐integral inequality is derived inspired by Wirtinger‐based single‐integral inequality. Using the advanced integral inequalities, the reciprocally convex combination techniques and necessary slack variables, together with extracting a condition for the positive definiteness of the Lyapunov functional, novel stability criteria, have been established for the system. The effectiveness of the criteria is evaluated via 2 numerical examples. The results indicate that more complex stability criteria not only improve the stability region but also bring computational expenses. |
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| Keywords: | interval time‐varying delay linear matrix inequality Lyapunov Krasovskii method Wirtinger‐based integral inequalities |
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