controllability conditions
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Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1955
Author(s):  
Jerzy Klamka

In the paper semilinear, finite-dimensional, control systems with multiple time variable point delays in admissible controls are considered. Using Rothe’s fixed-point theorem, sufficient controllability conditions are formulated. The results of the paper are generalization to many time variable delays in control, of the results published recently.


2020 ◽  
Vol 7 (1) ◽  
pp. 126-139
Author(s):  
Hugo Leiva ◽  
Dalia Cabada ◽  
Rodolfo Gallo

AbstractIn this paper, we prove that the controllability of time varying linear system is preserved if we add impulses, delay and nonlocal conditions on it. In order to do that, we assume some conditions on the non-linear terms and apply the Rothe’s fixed point theorem to obtain the main result. In other words, we find sufficient controllability conditions for the semilinear system under the influence of impulses, delay, and nonlocal conditions.


2019 ◽  
Vol 64 (10) ◽  
pp. 4223-4228 ◽  
Author(s):  
Yuqing Hao ◽  
Zhisheng Duan ◽  
Guanrong Chen ◽  
Fen Wu

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 71 ◽  
Author(s):  
Olga Tsekhan

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.


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