Geodesic
On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays
Kybernetika, Tome 55 (2019) no. 4, pp. 675-689.

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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.
DOI : 10.14736/kyb-2019-4-0675
Classification : 34G20, 93B05, 93C05, 93C10
Keywords: fractional systems; semilinear control systems; Rothe's fixed point theorem; delays in control; pseudo-transition matrix; the Caputo derivative 
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     title = {On application of {Rothe's} fixed point theorem to study the controllability of fractional semilinear systems with delays},
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Sikora, Beata. On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays. Kybernetika, Tome 55 (2019) no. 4, pp. 675-689. doi : 10.14736/kyb-2019-4-0675. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-4-0675/

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