The Lyapunov functionals method in stability problems for functional differential equations

DOI10.1134/S0005117909090021zbMath1182.93096MaRDI QIDQ1040514

A. S. Andreev

Publication date: 24 November 2009

Published in: Automation and Remote Control (Search for Journal in Brave)

zbMATH Keywords

functional differential equationsfirst and second (or direct) Lyapunov methodsnonlinear PDE stability

Mathematics Subject Classification ID

Lyapunov and storage functions (93D30) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Research exposition (monographs, survey articles) pertaining to systems and control theory (93-02) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30)

Related Items

Estimates for solutions to a class of nonlinear time-varying delay systems, Method of limit differential equations for nonautonomous discontinuous systems, Unnamed Item, The invariance principle for nonautonomous differential equations with discontinuous right-hand side, On the exponential stability of solutions of periodic systems of the neutral type with several delays, Method of limiting differential inclusions and asymptotic behavior of systems with relay controls, On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation, Lyapunov functional method in the stability problem of Volterra integro-differential equations with infinite delay, Invariance principle for nonautonomous functional-differential equations with discontinuous right-hand sides, Estimates for exponential decay of solutions to one class of nonlinear systems of neutral type with periodic coefficients, Global dynamics of one class of nonlinear nonautonomous systems with time-varying delays, Limit differential inclusions and the invariance principle for nonautonomous systems, LMI and SDP technique for stability analysis of nonlinear delay systems subject to constraints, Stabilization of the preset motions of a holonomic mechanical system without velocity measurement, Estimates for solutions to a class of nonautonomous systems of neutral type with unbounded delay, Method of limiting differential inclusions for nonautonomous discontinuous systems with delay, Estimates of the Exponential Decay of Solutions to Linear Systems of Neutral Type with Periodic Coefficients, On the Stability and Stabilization Problems of Volterra Integro-Differential Equations, On the Robust Stability of Solutions to Periodic Systems of Neutral Type, On stability of solutions to neutral type systems

Cites Work

• Stabilization of the motions of controlled mechanical systems by a regulator with delay
• Stability properties for functional differential equations with infinite delay
• On the stability problem for functional differential equations with infinite delay
• Method of Lyapunov functionals for systems with aftereffect
• On stabilization of the controlled mechanical systems
• The stability of motions of hereditary systems with infinite delay
• Perturbation theorems for functional differential equations with infinite delay via limiting equations
• Stability with respect to a part of the variables for a system with delay
• Functional differential equations and Jensen's inequality
• Stability theorems for nonautonomous functional differential equations by Lyapunov functionals
• On partial stability of differential equations with time delay
• On nonuniform asymptotic stability for nonautonomous functional differential equations
• Functional differential equations with infinite delay
• Stability theory and the existence of periodic solutions and almost periodic solutions
• Theory of functional differential equations. 2nd ed
• Topological dynamics of an ordinary differential equation
• Stability theory by Liapunov's direct method
• Uniform asymptotic stability via the limiting equations
• Annulus arguments in the stability theory for functional differential equations
• On the stability of invariant sets of functional differential equations.
• Families of Lyapunov-Krasovskiĭ functionals and stability for functional-differential equations
• On the partial equiasymptotic stability in functional differential equations
• On the asymptotic stability for functional differential equations by Lyapunov functionals.
• On the location of positive limit sets for autonomous functional differential equations with infinite delay
• Asymptotic stability without uniform stability: Almost periodic coefficients
• Uniformly asymptotic stability and total stability
• Equations with unbounded delay: a survey
• On partial stability for delay systems
• Uniform Asymptotic Stability in Functional Differential Equations
• On the asymptotic stability in functional differential equations
• Weakening the condition W1(|ø;(0)|) ≤ V(t, ø) ≤ W2(‖ø‖) for uniform asymptotic stability
• An example on the asymptotic stability for functional differential equations
• On the stability of nonautonomous functional differential equation
• On the asymptotic stability by lyapunov functionals with semidefinite derivatives
• Marachkov type stability results for functional differential equations
• Asymptotic Stability in Functional Differential Equations by Liapunov Functionals
• A STABILITY THEOREM FOR FUNCTIONAL-DIFFERENTIAL EQUATIONS
• The method of Lyapunov functionals for linear difference-differential systems with almost-periodic coefficients
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item