Exponential stability of linear systems under a class of Desch-Schappacher perturbations

2021/07/26 by Safae El Alaoui, Mohamed Ouzahra, Alaoui, Safae El +1
Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.12195

openalex publication_date 2021/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the uniform exponential stability of the system (dx(t))/(dt)=Ax(t)-ρBx(t), (ρ>0), where the unbounded operator A is the infinitesimal generator of a linear C₀-semigroup of contractions S(t) in a Hilbert space X and B is a Desch-Schappacher operator. Then we give sufficient conditions for exponential stability of the above system. The obtained stability result is then applied to show the uniform exponential stabilization of bilinear partial differential equations.

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