Perturbing uniform asymptotically stable nonlinear systems

DOI10.1016/0022-0396(69)90004-7zbMath0182.12103OpenAlexW1978092242MaRDI QIDQ2535307

James A. Yorke, Aaron Strauss

Publication date: 1969

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(69)90004-7

zbMATH Keywords

ordinary differential equations

Related Items (36)

A new concept of stability, \(M_ 0\)-stability ⋮ Uniform asymptotic stability implies exponential stability for nonautonomous half-linear differential systems ⋮ Decay mild solutions of fractional differential hemivariational inequalities ⋮ Feedback control for the nuclear reactors ⋮ Non-uniform asymptotic stability for the damped linear oscillator ⋮ Uniform asymptotic stability in perturbed differential equations ⋮ Perturbing almost periodic differential equations ⋮ Remarks on the preservation of uniform stability from a linear system to its perturbed system ⋮ Identifying Perturbations Which Preserve Asymptotic Stability ⋮ Development of the direct Lyapunov method for functional-differential equations with infinite delay ⋮ Linearization and asymptotic behavior ⋮ A note on the perturbing uniform asymptotically stable systems ⋮ Remarks on the asymptotic behavior of the solutions of certain non-autonomous differential equations ⋮ On the principle of reduction for the nonlinear delay systems ⋮ On the boundedness of solutions of perturbed linear systems ⋮ On the boundedness properties of a perturbed nonlinear system ⋮ Stability of impulsively perturbed systems ⋮ On the uniqueness of solutions in the hull ⋮ Weighted bounds on solutions of perturbed systems of differential equations ⋮ Asymptotic stabilization of a system of coupled \(n\)th-order differential equations with potentially unbounded high-frequency oscillating perturbations ⋮ Lyapunov theory and perturbation of stable and asymptotically stable systems ⋮ On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations ⋮ Robustness of ISS systems to inputs with limited moving average: Application to spacecraft formations ⋮ A problem of rated stability of dynamic systems ⋮ Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions. II ⋮ On the exponentially asymptotic stability of a perturbed nonlinear system ⋮ Perturbations of nonlinear systems of differential equations. III ⋮ Uniformly asymptotic stability and total stability ⋮ The linearized uniform asymptotic stability of evolution differential equations ⋮ Perturbation theorems for nonlinear systems of ordinary different equations ⋮ Global asymptotic behaviour of functional differential equations of the neutral type ⋮ Uniform asymptotic stability of time-varying damped harmonic oscillators ⋮ Perturbation theorems for functional differential equations with infinite delay via limiting equations ⋮ Asymptotically Autonomous Multivalued Differential Equations ⋮ The topological dynamics of perturbed differential equations ⋮ Continuability of solutions of perturbed differential equations

Cites Work

• Contributions to stability theory
• Differential equations: Stability, oscillations, time lags
• Asymptotic behavior of nonlinear delay-differential equations
• Perturbation theorems for ordinary differential equations
• Integral stability
• Nonlinear Differential Equations with Forcing Terms
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Perturbing uniform asymptotically stable nonlinear systems