On shift of the Lyapunov spectrum for linear stationary control systems in Banach spaces

2018 ◽  
Author(s):  
Vasilii Aleksandrovich Zaitsev
Keyword(s):  
Control Systems ◽  
Banach Spaces ◽  
Lyapunov Spectrum ◽  
Stationary Control

On exact controllability of linear perturbed boundary systems: a semigroup approach

2020 ◽  
Vol 37 (4) ◽  
pp. 1548-1573
Author(s):  
Marieme Lasri ◽  
Hamid Bounit ◽  
Said Hadd
Keyword(s):  
Control System ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exact Controllability ◽  
Dimensional Control ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Semigroup Approach ◽  
Perturbed Linear Systems

Abstract The purpose of this paper is to investigate the robustness of exact controllability of perturbed linear systems in Banach spaces. Under some conditions, we prove that the exact controllability is preserved if we perturb the generator of an infinite-dimensional control system by appropriate Miyadera–Voigt perturbations. Furthermore, we study the robustness of exact controllability for perturbed boundary control systems. As application, we study the robustness of exact controllability of neutral equations. We mention that our approach is mainly based on the concept of feedback theory of infinite-dimensional linear systems.

Controllability of Abstract Systems of Fractional Order

2015 ◽  
Vol 18 (6) ◽  
Author(s):  
Therese Mur ◽  
Hernán R. Henríquez
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Integral Equation ◽  
Control Systems ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Fractional Integral ◽  
First Order ◽  
Fractional Integral Equation ◽  
Fractional Differential

AbstractIn this paper we are concerned with the controllability of control systems governed by a fractional differential equation in Banach spaces. Using the properties of the Mittag-Leffler function we generalize to these systems a result of Korobov and Rabakh, which was established for first order systems. We apply our results to study the controllability of a system modeled by a fractional integral equation in a Hilbert space.

scholarly journals On exponential dichotomy in Banach spaces

1981 ◽  
Vol 23 (2) ◽  
pp. 293-306 ◽  
Author(s):  
Mihail Megan ◽  
Petre Preda
Keyword(s):  
Banach Space ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Linear Control ◽  
Linear Control Systems

In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems. The obtained results are generalizations of well-known results of W.A. Coppel, J.L. Massera and J.J. Schäffer, K.J. Palmer.

scholarly journals Measurable multifunctions and their applications to convex integral functionals

1989 ◽  
Vol 12 (1) ◽  
pp. 175-191 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Control Systems ◽  
Banach Spaces ◽  
Time Dependent ◽  
Linear Control ◽  
Linear Control Systems ◽  
Integral Functionals ◽  
Control Constraints ◽  
Infinite Dimensional ◽  
Measurable Multifunctions

The purpose of this paper is to establish some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functionals defined on Lebesgue-Bochner spaces. In this process we also obtain a characterization of separable dual Banach spaces using multifunctions and we present some generalizations of the classical “bang-bang” principle to infinite dimensional linear control systems with time dependent control constraints.

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