Technical Stability of Nonlinear Time-Varying Systems With Small Parameters

CHU Tian-guang; WANG Zhao-lin

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CHU Tian-guang, WANG Zhao-lin. Technical Stability of Nonlinear Time-Varying Systems With Small Parameters[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1140-1146.

Citation:

CHU Tian-guang, WANG Zhao-lin. Technical Stability of Nonlinear Time-Varying Systems With Small Parameters[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1140-1146.

Citation:

CHU Tian-guang, WANG Zhao-lin. Technical Stability of Nonlinear Time-Varying Systems With Small Parameters[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1140-1146.

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Technical Stability of Nonlinear Time-Varying Systems With Small Parameters

CHU Tian-guang¹,
WANG Zhao-lin²

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

Received Date: 1999-08-03
Rev Recd Date: 2000-05-25
Publish Date: 2000-11-15

Abstract

Abstract

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.
- nonlinear time-varying system,
- small parameter,
- technical stability,
- vector comparison principle,
- reduced system,
- linearization technique,
- exponential asymptotic stability

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References(11)

References

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