Phat, V. N.; Khongtham, Y.; Ratchagit, K. LMI approach to exponential stability of linear systems with interval time-varying delays. (English) Zbl 1230.93076 Linear Algebra Appl. 436, No. 1, 243-251 (2012). Summary: This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with the Newton-Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of Linear Matrix Inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results. Cited in 29 Documents MSC: 93D20 Asymptotic stability in control theory 93C05 Linear systems in control theory 15A09 Theory of matrix inversion and generalized inverses 52A10 Convex sets in \(2\) dimensions (including convex curves) 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory Keywords:exponential stability; interval delay; Lyapunov function; linear matrix inequalities PDFBibTeX XMLCite \textit{V. N. Phat} et al., Linear Algebra Appl. 436, No. 1, 243--251 (2012; Zbl 1230.93076) Full Text: DOI References: [1] de Oliveira, M. C.; Geromel, J. C.; Hsu, L., LMI characterization of structural and robust stability: the discrete-time case, Linear Algebra Appl., 296, 27-38 (1999) · Zbl 0949.93063 [2] Phat, V. N.; Nam, P. T., Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function, Int. J. Control, 80, 1333-1341 (2007) · Zbl 1133.93358 [3] Phat, V. N.; Niamsup, P., A novel exponential stability condition of hybrid neural networks with time-varying delay, Vietnam J. Math., 38, 341-351 (2010) · Zbl 1223.34104 [4] Sun, Y. J., Global stabilizability of uncertain systems with time-varying delays via dynamic observer-based output feedback, Linear Algebra Appl., 353, 91-105 (2002) · Zbl 1001.93066 [5] Kwon, O. M.; Park, J. H., Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays, Appl. Math. Comput., 208, 58-68 (2009) · Zbl 1170.34054 [6] Shao, H., New delay-dependent stability criteria for systems with interval delay, Automatica, 45, 744-749 (2009) · Zbl 1168.93387 [7] Sun, J.; Liu, G. P.; Chen, J.; Rees, D., Improved delay-range-dependent stability criteria for linear systems with time-varying delays, Automatica, 46, 466-470 (2010) · Zbl 1205.93139 [8] Zhang, W.; Cai, X.; Han, Z., Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations, J. Comput. Appl. Math., 234, 174-180 (2010) · Zbl 1185.93111 [9] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of Time-Delay Systems (2003), Birkhauser: Birkhauser Boston · Zbl 1039.34067 [10] Wang, Y.; Xie, L.; de Souza, C. E., Robust control of a class of uncertain nonlinear systems, Syst. Control Lett., 19, 139-149 (1992) · Zbl 0765.93015 [11] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004 [12] Hale, J. K.; Verduyn Lunel, S. M., Introduction to Functional Differential Equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.