A new stability test for nonlinear nonautonomous systems☆

GIL, M

doi:10.1016/s0005-1098(04)00227-4

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then any solution x(t) of (1.1) satisfies the inequality |x(t)| ≤ const e γt (t ≥ 0). This result is very useful for various applications; see for instance [6,7] and the references therein. Condition (1.2) is a refinement of (1.10), since (1.10) does not allow the roots to intersect.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 74%

Estimates for the Green functions of nonautonomous higher order differential equations

Gil’

2009

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 74%

Estimates for the Green functions of nonautonomous higher order differential equations

Gil’

2009

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Note that we obtain new exponential stability conditions for equations with measurable coefficients. In most stability conditions it was assumed that b(t) ≡ b > 0 [19,20,28,33,35], b(t) ≥ 0 is a differentialble function [8,21,23,24,31] or some restrictions like slow varying coefficients [13,15,16] were imposed. We consider here equation (1.1) without usual restrictions on parameters of the equations, the coefficients are even not required to be continuous.…”

Section: Introductionmentioning

confidence: 99%

Nonoscillation and Stability of the Second Order Ordinary Differential Equations with a Damping Term

Berezansky,

Braverman,

Domoshnitsky

2008

Preprint

View full text Add to dashboard Cite

In this paper we consider the linear ordinary equation of the second order £x(t) ≡ ẍ(t) + a(t) ẋ(t) + b(t)x(t) = f (t), (0.1) and the corresponding homogeneous equationNote that [α, β] is called a nonoscillation interval if every nontrivial solution has at most one zero on this interval. Many investigations which seem to have no connection such as differential inequalities, the Polia-Mammana decomposition (i.e. representation of the operator £ in the form of products of the first order differential operators), unique solvability of the interpolation problems, kernels oscillation, separation of zeros, zones of Lyapunov's stability and some others have a certain common basis -nonoscillation.Presumably Sturm was the first to consider the two problems which naturally appear here: to develop corollaries of nonoscillation and to find methods to check nonoscillation. In this paper we obtain several tests for nonoscillation on the semiaxis and apply them to propose new results on asymptotic properties and the exponential stability of the second order equation (0.2). Using the Floquet representations and upper and lower estimates of nonoscillation intervals of oscillatory solutions we deduce results on the exponential and Lyapunov's stability and instability of equation (0.2).

show abstract

A less conservative stability test for second-order linear time-varying vector differential equations

Wang

Zhong

2007

International Journal of Control

View full text Add to dashboard Cite

System stability and stability bounds play an essential role in control theory. This note is concerned with the exponential stability of a class of second-order linear time-varying vector differential equations with real piecewise continuous coefficient matrices. A less conservative explicit condition for stability of such a system is derived using the matrix measure theory and a more accurate upper bound for the decay exponent of its stable solution is established. Examples are included for illustration.

show abstract

A new stability test for nonlinear nonautonomous systems☆

Cited by 3 publications

References 0 publications

Estimates for the Green functions of nonautonomous higher order differential equations

Estimates for the Green functions of nonautonomous higher order differential equations

Nonoscillation and Stability of the Second Order Ordinary Differential Equations with a Damping Term

A less conservative stability test for second-order linear time-varying vector differential equations

Contact Info

Product

Resources

About