Trajectory-Based Local Approximations of Ordinary\ Differential\ Equations
- 1 January 2003
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 41 (6) , 1922-1945
- https://doi.org/10.1137/s0363012900370776
Abstract
The present paper introduces a new definition of local approximation for ordinary differential equations locally around an equilibrium point. This definition generalizes the well-known linear and homogeneous approximations. The approach is based on approximating trajectories near the origin. This concept of local approximation is applied to the study of local uniform asymptotic stability, leading to alternative proofs for and extensions of several existing stability results.Keywords
This publication has 20 references indexed in Scilit:
- Asymptotic methods in the stability analysis of parametrized homogeneous flowsAutomatica, 2000
- Practical stability and stabilizationIEEE Transactions on Automatic Control, 2000
- On exponential stability of nonlinear time-varying differential equationsAutomatica, 1999
- Time-varying homogeneous feedback: Design tools for the exponential stabilization of systems with driftInternational Journal of Control, 1998
- An Approximation Algorithm for Nonholonomic SystemsSIAM Journal on Control and Optimization, 1997
- Exponential stabilization of driftless nonlinear control systems using homogeneous feedbackIEEE Transactions on Automatic Control, 1997
- Averaging in Stability TheoryPublished by Springer Nature ,1993
- Nilpotent and High-Order Approximations of Vector Field SystemsSIAM Review, 1991
- Limit processes in ordinary differential equationsZeitschrift für angewandte Mathematik und Physik, 1987
- Integral averaging and bifurcationJournal of Differential Equations, 1977