A control method for a class of minimum-phase fractional-delay systems based on shaping the sensitivity function

This paper deals with the boundary control problem for a certain class of linear infinite-dimensional systems commonly known as fractional-delay systems. It is assumed that the systems under consideration are, in general, described by multi-valued transfer functions. In this paper, we restrict our studies to a class of multi-valued transfer functions which are defined on a Riemann surface with limited number of Riemann sheets where the origin is a branch point. The proposed controller design algorithm is based on shaping the sensitivity function. Contrary to many other methods which approximate the underlying infinite-dimensional system by a finite-dimensional one and then apply a classical controller design algorithm, the proposed method directly obtains the controller without such an approximation. In the proposed method, however, the order-reduction algorithm is applied to the resulted infinite-dimensional controller at the final stage and consequently the resulted closed-loop system is much more reliable. The proposed method is applicable to both stable and unstable minimum-phase plants which have limited number of unstable poles. Two examples are used to confirm the efficiency of the proposed method and the results are discussed.