This paper presents a method of designing a state-observer based modified repetitive-control system that provides a given H? level\nof disturbance attenuation for a class of strictly proper linear plants. Since the time delay in a repetitive controller can be treated\nas a kind of disturbance, we convert the system design problem into a standard state-feedback H? control problem for a linear\ntime-invariant system. The Lyapunov functional and the singular-value decomposition of the output matrix are used to derive\na linear-matrix-inequality (LMI) based design algorithm for the parameters of the feedback controller and the state-observer. A\nnumerical example demonstrates the validity of the method.
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