Stability of multivariable repetitive control systems. Stability condition and class of stabilizing controllers.:Stability Condition and Class of Stabilizing Controllers

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The repetitive control system is a neutral or retarded type time-lag system, which includes a model or approximate model of a generator of periodic signals in the closed-loop. This paper investigates the stability to clarify the design tradeoff between the stability and the frequency band to be tracked. A sufficient condition of the exponential stability is presented and a class of stabilizing controllers including low pass filters is derived by factorization approach. It is also shown that the results obtained here can be directly applied to the analysis and synthesis of learning or iterative control systems and PI-type control systems.
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