A nonlinear version of Halanay's inequality for the uniform convergence to the origin
Pierdomenico Pepe
Abstract
<p style='text-indent:20px;'>A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.</p>
Topics & Concepts
MathematicsConvergence (economics)Nonlinear systemBounded functionUniform convergenceExponential stabilityApplied mathematicsLyapunov functionStability (learning theory)Forcing (mathematics)Mathematical analysisUniform boundednessComputer scienceBandwidth (computing)Machine learningEconomicsQuantum mechanicsComputer networkPhysicsEconomic growthStability and Controllability of Differential EquationsStability and Control of Uncertain SystemsControl and Stability of Dynamical Systems