title: Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems.
abstract: In this paper, controllability and observability matrices for pseudo upper or lower triangular multi-order fractional systems are derived. It is demonstrated that these systems are controllable and observable if and only if their controllability and observability matrices are full rank. In other words, the rank of these matrices should be equal to the inner dimension of their corresponding state space realizations. To reduce the computational complexities, these matrices are converted to simplified matrices with smaller dimensions. Numerical examples are provided to show the usefulness of the mentioned matrices for controllability and observability analysis of this case of multi-order fractional systems. These examples clarify that the duality concept is not necessarily true for these special systems.
authors.affiliation: Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran. Electronic address: iman.hassanzadeh@iaukhsh.ac.ir.
authors.forename: Iman
authors.initials: I
authors.lastname: Hassanzadeh
authors.affiliation: Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran. Electronic address: tabatabaei@iaukhsh.ac.ir.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Tabatabaei
keywords: Controllability; Fractional order systems; Multi-order fractional systems; Observability