Description and realization for a class of irrational transfer functions with nonzero initial instant

The realization of a class of irrational transfer functions is studied in this work. Such transfer functions are essentially fractional order systems. The well-known frequency distributed model method is actually the true state space model of fractional order systems. From this, the state space model of the considered transfer functions are developed. By employing the discretization scheme, the infinite dimensional equivalent model is approximated subsequently. Notably, the constraint on the zero initial instant of Laplace transform is removed successfully. The merits of the elaborated results are carefully evaluated by three illustrative examples.