Obtaining Controllable Pseudo-Upper and Lower Triangular Multi-Order State-Space Realizations from a Special Case of Incommensurate Fractional-Order Transfer Functions

This paper presents a methodology for finding a pseudo-upper or lower triangular state-space realization (SSR) from an incommensurate fractional-order transfer function. This SSR is obtained for a particular case of incommensurate fractional-order systems that can be represented by pseudo-upper or lower triangular multi-order state-space equations, which are derived by drawing the block diagram of the transfer functions. The obtained realization is very similar to the controllability canonical form for ordinary transfer functions. It is demonstrated that the obtained realization is controllable. Thus, the state feedback controllers can be systematically designed for these systems.