Sufficient criteria for stabilization properties in Banach spaces

2021/08/20 by Michela Egidi, Dennis Gallaun, Egidi, Michela +5 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.09028

openalex publication_date 2021/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study abstract sufficient criteria for open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces given by an uncertainty principle and a dissipation estimate. For stabilizability these estimates are only needed for a single spectral parameter and, in particular, their constants do not depend on the growth rate w.r.t. this parameter. Our result unifies and generalizes earlier results obtained in the context of Hilbert spaces. As an application we consider fractional powers of elliptic differential operators with constant coefficients in L_p(ℝ^d) for p∈ [1,∞) and thick control sets.

Cited by

• Stabilizability of neural fields from thick subsets

Related

• Sufficient criteria for stabilization properties in Banach Spaces
• Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach
• Feedback stabilization of linear and bilinear unbounded systems in Banach space
• Perturbations of Admissibility, Exact Controllability, Exact Observability and Regularity
• Characterizations of complete stabilizability