Controllability and observability behaviors of a non-homogeneous conformable fractional dynamical system compatible with some electrical applications

In this work, we discuss the controllability and observability behaviors of a non-homogeneous conformable fractional dynamical system (C-FDS) based on the conformable fractional exponential matrix (C-FEM) and fractional Grammian matrix (FGM). Moreover, the nice relationships between controllability, observability, and stability for non-homogeneous C-FDS are derived. To demonstrate the effectiveness of our obtained results, we present the general solutions (GSs), controllability, observabilities and stabilities to three attractive physical and engineering problems related to compatibility with conformable fractional electrical circuits (C-FECs). Finally, the fractional and classical behaviors of each problem have been covered, respectively, when alpha = 1/2 and alpha = 1. (C) 2021 THE AUTHOR. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

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This work discusses the controllability and observability behaviors of non-homogeneous conformable fractional dynamical systems, deriving the relationships between controllability, observability, and stability. The effectiveness of the results is demonstrated through solutions to physical and engineering problems, with comparisons between fractional and classical behaviors under different circumstances.