Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions
Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions
We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov's sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some sufficient conditions for a system to be stabilized by means of a feedback law of the Jurdjevic-Quinn...
Stability and ultimate boundedness of solutions to certain third-order differential equations.
Stability at constantly acting disturbances of abstract differential equations with the right-hand sides smooth in the time variable
Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order
Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations
In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.
Stability for a family of systems of differential equations with sectionally continuous right-hand sides.
Stability for parameter estimation in two point boundary value problems.
Stability implications on the asymptotic behavior of nonlinear systems.
Stability in generalized processes
Stability in the large of certain non-linear systems of differential equations of order three
Stability of a class of adaptive nonlinear systems
This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear...
Stability of a linear oscillator with variable parameters.
Stability of a model for the Belousov-Zhabotinskij reaction
The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.
Stability of a two-strain tuberculosis model with general contact rate.
Stability of abstract differential equations at constantly acting disturbances
Stability of abstract differential equations with the right-hand side smooth in the time variable
Stability of Attractivity Regions for Autonomous Functional Differential Equations.
Stability of Caputo fractional differential equations by Lyapunov functions
The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based on the new...
Stability of higher order singular points of Poisson manifolds and Lie algebroids
We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...