Phase- Variable Canonical State-Space Realizations and Initializations for Linear Time-Invariant Multi-term Fractional Differential Equations

This paper is devoted to realizing and initializing state-space realizations for linear time-invariant multi-term fractional differential equations. For this purpose, two types of companion state-space realizations are proposed for linear time-invariant multi-term fractional-order systems: a) commensurate phase-variable canonical state space, and b) incommensurate phase-variable canonical state space. Furthermore, a method of initializing the proposed state-space representations is proposed for dynamical systems subject to feasible initial conditions. The advantages of the proposed representations are shown in an illustrative example.