Stabilization and Practical Asymptotic Stability of Abstract Differential Equations

2016/08/05 by H. Damak, Hanen Damak, M. A. Hammami +1
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · doi:10.1080/01630563.2016.1211681

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.

Related

• Lyapunov methods for input-to-state stability of time-varying evolution equations
• Control in finite and infinite dimension
• Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach
• Finite-Time Stabilization of a Class of Nonlinear Systems in Hilbert Space
• On Finite- and Fixed-Time Stabilization of Abstract Nonlinear Systems with Well-Posedness Guarantees