Controllability and observability of conformable fractional finite dimensional linear systems

Abstract

In this research paper, we investigate the controllability and observability of continuous-time fractional dynamical systems. The characterisation of all fractional continuous one-parameter semi groups on a finite dimensional vector space as fractional matrix-valued exponential functions is given. This characterisation is used to express the solution of continuous-time fractional dynamical system. Furthermore, we analyse controllability and observability of linear conformable fractional systems in the mathematical context of linear operators on a finite dimensional vector space. By defining the controllability and observability maps, we establish necessary and sufficient conditions for controllability and observability of this type of systems. We also present the Hautus test for controllability and observability, and introduce controllability and observability Gramians, both for finite and infinite time interval. Finally, we present several illustrative applications and examples to validate all the obtained results.