<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative <italic>U</italic>-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.</p></abstract>

The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.

Controllability criteria for time–delay fractional systems with a retarded state

Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is...

Controllability criteria for time–delay fractional systems with a retarded state

Published Online: Sep 29, 2016

Page range: 521 - 531

Received: Dec 16, 2015

Accepted: May 10, 2016

DOI: https://doi.org/10.1515/amcs-2016-0036

Keywords
fractional dynamical systems, controllability, delays in the state, constraints, pseudo-transition matrix, Caputo derivative

© 2016 Beata Sikora, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Controllability criteria for time–delay fractional systems with a retarded state

Published Online: Sep 29, 2016

Page range: 521 - 531

Received: Dec 16, 2015

Accepted: May 10, 2016

DOI: https://doi.org/10.1515/amcs-2016-0036

Keywordsfractional dynamical systems, controllability, delays in the state, constraints, pseudo-transition matrix, Caputo derivative

© 2016 Beata Sikora, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fractional dynamical systems, controllability, delays in the state, constraints, pseudo-transition matrix, Caputo derivative