Realization theory of infinite-dimensional linear systems. Part I

1981 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
Yutaka Yamamoto
Keyword(s):  
Linear Systems ◽  
Realization Theory ◽  
Infinite Dimensional

$H^2 $-Functions and Infinite-Dimensional Realization Theory

1975 ◽  
Vol 13 (1) ◽  
pp. 221-241 ◽  
Author(s):  
J. S. Baras ◽  
R. W. Brockett
Keyword(s):  
Realization Theory ◽  
Infinite Dimensional

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.

scholarly journals Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd2π-Periodic Functions

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Tamás Kalmár-Nagy ◽  
Márton Kiss
Keyword(s):  
Nonlinear Systems ◽  
Linear Operator ◽  
Linear Systems ◽  
Chaotic Dynamics ◽  
Periodic Points ◽  
Complex Behavior ◽  
Periodic Functions ◽  
Infinite Dimensional ◽  
Backward Shift ◽  
Principal Value

Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequencesl2displays chaotic dynamics. Here we construct the corresponding operatorCon the space of2π-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories ofC.

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