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《应用数学和力学(英文版)》 2000-11
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TECHNICAL STABILITY OF NONLINEAR TIME-VARYING SYSTEMS WITH SMALL PARAMETERS

CHU Tian_guang 1, WANG Zhao_lin 2 (1 Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P R China; 2 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P R China)  
Technical stability allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time_varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time_varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.
【Fund】: theNationalNaturalScienceFoundationofChina (1 9872 0 0 5 ) ;theResearch FundfortheDoctoralProgramofHigherEducation (970 0 0 1 3
【CateGory Index】: O175.21
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