Abstract
In this paper we discuss a design of model following control systems (MFCS) for discrete time systems and the robust stability conditions. In case that a controlled object has unstable zeros, it has been difficult to design a stable MFCS by using conventional methods. The reason is that a characteristic polynomial of the closed loop system involves a characteristic polynomial of unstable zeros. In this paper we use the method to involve a zero characteristic polynomial in control input signals. This method is one of a signal synthesis. Under the condition that all of the future values of reference inputs are known, we can synthesize bounded signals which are necessary for control inputs. Futhermore we discuss robust stability conditions when the transfer function of a controlled object has errors. We use a formulation whose errors exist in a numerator matrix and a denominator matrix of a right coprime decomposition as additive forms. Such a formulation does not lose the generality, but makes quantitative analysis of robustness easy. From Rouche's theorem and norm calculations of matrices, we obtain robust stability condition. In robust analysis of discrete time system by this paper's method, there is no limitation of polynomial degree of error matrices. This property does not exist in continuous time systems. So we can expand this paper's robust stability conditions to the case that error matrices are general analytic functions.
