Kybernetika 55 no. 4, 675-689, 2019

On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays

Beata SikoraDOI: 10.14736/kyb-2019-4-0675

Abstract:

The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function $f$. The relative controllability of the presented semilinear system is discussed. Rothe's fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A~control that steers the semilinear system from an initial complete state to a final state at time $t>0$ is presented. A numerical example is provided to illustrate the obtained theoretical results and a practical example is given to show a possible application of the study.

Keywords:

the Caputo derivative, delays in control, fractional systems, semilinear control systems, Rothe's fixed point theorem, pseudo-transition matrix

Classification:

93B05, 93C05, 93C10, 34G20

paper.pdf

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