Repetitive control system: A new type servo system for periodic exogenous signals. (English) Zbl 0662.93027

Authors’ summary: “In this paper, a new control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time-lag systems. Synthesis algorithms are presented both by the state-space approach and the factorization approach. In the former approach, the technique of the Kalman filter and perfect regulation is utilized, while coprime factorization over the matrix ring of proper stable rational functions and the solution of the Hankel norm approximation are used in the latter one”.
Reviewer: T.Tadumadze


93B50 Synthesis problems
93B40 Computational methods in systems theory (MSC2010)
93D99 Stability of control systems
15A23 Factorization of matrices
93E11 Filtering in stochastic control theory
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