Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

• Published in: IEEE transactions on automatic control Vol. 60; no. 10; pp. 2768 - 2772
• Main Authors: Zeng, Hong-Bing, He, Yong, Wu, Min, She, Jinhua
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Automatic control; Criteria; Delay; Delays; Educational institutions; Free-matrix-based integral inequality; Inequalities; Integrals; Linear matrix inequalities; Lyapunov-Krasovskii functional; Stability; Stability analysis; Stability criteria; Symmetric matrices; time delay system; time-varying delay; Transformations; Upper bound; Vectors; Free-matrix-based integral inequality; time-varying delay; time delay system; Lyapunov–Krasovskii functional; stability
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2404271

The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.