Liu, Yubin; Feng, Weizhen Razumikhin-Lyapunov functional method for the stability of impulsive switched systems with time delay. (English) Zbl 1165.34411 Math. Comput. Modelling 49, No. 1-2, 249-264 (2009). Summary: This paper investigates the uniform stability and the uniform asymptotical stability of impulsive switched systems with time delay. By employing the method of Razumikhin-Lyapunov functional, several Razumikhin-type theorems of uniform stability and uniform asymptotical stability are established, which improve some of the existing results. Several examples are also given to illustrate the results. Cited in 11 Documents MSC: 34K20 Stability theory of functional-differential equations 34K45 Functional-differential equations with impulses Keywords:Lyapunov functional; Razumikhin technique; switched systems; uniform stability; uniform asymptotical stability PDFBibTeX XMLCite \textit{Y. Liu} and \textit{W. Feng}, Math. Comput. Modelling 49, No. 1--2, 249--264 (2009; Zbl 1165.34411) Full Text: DOI References: [1] Liberzon, Daniel; Stephen Morse, A., Basic problems in stability and design of switched systems, IEEE Control Systems, 59-70 (1999) · Zbl 1384.93064 [2] Lakshmikantham, V.; Liu, Xinzhi, Impulsive hybrid systems and stability theory, Dynamic Systems and Applications, 7, 1-10 (1998) · Zbl 0901.34018 [3] Sun, Ye; Michel, Anthony N.; Zhai, Guisheng, Stability of discontinuous retarded functional differential equations with applications, IEEE Transactions on Automatic Control, 5, 1090-1105 (2005) · Zbl 1365.34127 [4] Wen, Lizhi, The method of Lyapunov functionals for stability of functional differential equations, Ke Xue Tong Bao, China, 29, 533-537 (1984) [5] Shen, J. H., Razumikhin techniques in impulsive functional differential equations, Nonlinear Analysis, 36, 119-130 (1999) · Zbl 0939.34071 [6] Yan, Jurang; Shen, Jianhua, Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions, Nonlinear Analysis, 37, 245-255 (1999) · Zbl 0951.34049 [7] Liu, Xinzhi; Ballinger, G., Uniform asymptotic stability of impulsive delay differential equations, Computers and Mathematics with Applications, 41, 903-915 (2001) · Zbl 0989.34061 [8] Luo, Zhiguo; Shen, Jianhua, New Razumikhin type theorems for impulsive functional differential equations, Applied Mathematics and Computation, 125, 375-386 (2002) · Zbl 1030.34078 [9] Liu, Kaien; Fu, Xilin, Stability of functional differential equations with impulses, Journal of Mathematical Analysis and Applications, 328, 830-841 (2007) · Zbl 1118.34079 [10] Liu, Xinzhi; Wang, Qing, The methold of Lyapunov functionals and exponential stability of impulsive systems with time delay, Nonlinear Analysis, 66, 1465-1484 (2007) · Zbl 1123.34065 [11] Hale, J. K., Order Differential Equations (1969), Wiley-Interscience: Wiley-Interscience New York · Zbl 0186.40901 [12] Hale, Jack, Theory of Functional Differential Equations (1971), Springer-Verlag: Springer-Verlag New York · Zbl 0222.34063 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.