\(H_\infty\) controller design for an observer-based modified repetitive-control system (Q275985)

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