On the controllability and observability of fractional proportional linear systems

Abstract

This paper deals with generalised Caputo fractional proportional linear time-invariant systems in a finite-dimensional space. The Laplace transformation method ensures the analytical solution of the desired fractional linear time-invariant systems. The present article presents the necessary and sufficient conditions for controllability and observability of the generalised Caputo proportional fractional linear time-invariant systems. These two properties can play a more fundamental role in system analysis before controller and observer designs are engaged. Moreover, we have acquired the criterion for generalised Caputo proportional fractional linear time-invariant systems as Kalman rank conditions. Some numerical examples are presented to show the applicability of the paper to demonstrate our findings. Finally, we derive the necessary and sufficient controllability conditions for the generalised Caputo proportional fractional-order nonlinear Chua's electric circuit.

Keywords:

• Controllability
• observability
• fractional proportional derivative
• time-invariant system
• Chua's circuit

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Khizra Bukhsh

Khizra Bukhsh Received her MSc. degree from Ghazi University, Dera Ghazi Khan, Pakistan in 2017, and MPhil degree from Bahauddin Zakariya University, Multan, Pakistan, in 2019, respectively, and currently she is Ph.D Schalor at Bahauddin Zakariya University, Multan, Pakistan. Presently, she is a lecturer at the Department of Mathematics, Ghazi University, Dera Ghazi Khan, Pakistan. Her current research interests include intelligent control systems and fractional calculus.

Awais Younus

Awais Younus Received his BS degree from Bahauddin Zakariya University, Multan, Pakistan in 2008, and PhD degree in Control systems from Govt. College University, Lahore, Pakistan, in 2013, respectively. Presently, he is Associate Professor at Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan. His current research interests include intelligent control systems and fractional calculus, interval analysis.