Input-to-state stability for time-varying delayed systems in Halanay-type inequality forms |
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| Institution: | 1. College of Science, Hunan University of Technology, Zhuzhou 412000, Hunan, P. R. China;2. Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, P. R. China;3. The Mork Family Department of Chemical Engineering and Materials Science, Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089 USA;1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China;2. Doctoral School FEIT, SS Cyril and Methodius University, 18 Rugjer Boskovic Str, Karpos 2, Skopje 1000, Republic of N. Macedonia;1. School of Mathematics, Southeast University, Nanjing 210096, PR China;2. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250358, PR China;3. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, PR China;1. School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. School of Automation, China University of Geosciences, Wuhan 430074, China;3. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China;1. College of Mathematics and Computer Science, Tongling University, Tongling, 244000, China;2. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, 212013, China |
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| Abstract: | This paper studies the input-to-state stability (ISS) for time-varying delayed systems (TVDS) in Halanay-type inequality forms. The time-delay in TVDS is allowed to be time-varying and unbounded. By introducing the notion of a uniform M-matrix, exponential ISS theorems are established respectively for continuous-time, discrete-time, and zero-order TVDS. The convergence rates of exponential ISS and ISS gains and their relation are subsequently estimated. These ISS theorems are less conservative and generalize the results of stability and ISS for Halanay-type inequalities in the literature. Moreover, necessary conditions of ISS are given for TVDS in Halanay-type equality forms. By specializing the ISS results to linear time-invariant delayed systems, the necessary and sufficient conditions of ISS are derived respectively. Three examples are given throughout the paper to illustrate the theoretical results. |
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