# zbMATH — the first resource for mathematics

On the extension of Rosenbrock’s theory in algebraic design of multivariable controllers. (English) Zbl 0635.93019
This paper is concerned with control system design methods by polynomial algebra. It is not based on right matrix fraction description, which is usually employed for control system design by polynomial algebra, but is based on Rosenbrock’s system theory. The controller structure is assumed as a linear feedback of the total state of the original plant and a dynamical precompensator. The conditions that the closed-loop transfer function exactly matches with the prescribed transfer function are given in two theorems, in which a set of controller parameters which yield exact matching is presented. The results are apparently quite different from those given in terms of right matrix fraction description: R(s) must be stable and $$T_ d(s)\xi_ T(s)$$ is proper, where R(s) is a numerator matrix of the plant, $$T_ d(s)$$ is a reference model transfer function and $$\xi_ T(s)$$ is an interactor of the plant. The reviewer thinks that the results presented in this paper must be equivalent to those given in terms of right matrix fraction description.
Reviewer: K.Ichikawa

##### MSC:
 93B25 Algebraic methods 93B50 Synthesis problems 93C35 Multivariable systems, multidimensional control systems 93C05 Linear systems in control theory
Full Text: