Stabilization and Practical Asymptotic Stability of Abstract Differential Equations. (2nd October 2016)

• Record Type: Journal Article
• Authors: Damak, H.; Hammami, M. A.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 10(2016)
• Page Start: 1235
• Page End: 1247
• Publication Date: 2016-10-02
• Subjects: Abstract differential equations -- controllability -- Lyapunov functions -- practical stability -- Ricatti equation -- stabilization; 34H15 -- 93B05 -- 12H20 -- 47H20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1211681
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This article studies the problem of stabilization of the infinite-dimension time-varying control systems in Hilbert spaces. We consider the problem of practical asymptotic stability with respect to a continuous functional for a class of abstract nonlinear infinite-dimensional processes with multivalued solutions on a metric space when the origin is not an equilibrium point. In the case of the existence of a differentiable Lyapunov functional, we obtain sufficient conditions for the practical stability of continuous semigroups in a Banach space.