Abstract
This paper presents a finite spectrum assignment procedure based upon the input-output relation for scalar systems with commensurate time-delays. This procedure is effective under the spectral controllability and the spectral observability of systems.
Existing procedures based upon state space realizations need matrix calculation, but this procedure needs only scalar calculation. It consists of the following two steps.
(1) To solve the polynomial Bezout equation consisting of denominator and numerator of the transfer function.
(2) To design control systems using the solution given in the spep (1).
In the step (1), the algorithm is based upon properties of polynomial ring in two variables. The solution can be obtained over polynomials with coefficients in a special ring of the finite Laplace transform. In step (2), it is possible to design output-feedback-type and observer-type control systems with a finite set of spectrum assigned.
