Robust H∞H∞ output-feedback control of systems with time-delay

The problem of designing robust dynamic output-feedback controllers for linear, continuous, time-invariant systems with uncertain time-delay in the measured output and/or the control input and with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state–space model of the system is described which permits reconstruction of its states. The resulting retarded model incorporates the uncertain parameters of the transfer function matrix in the state–space matrices and the uncertain time-delay that occurs in the control channel. To this model, the recent theory of robust H∞H∞ state-feedback control for retarded systems is applied. The theory is used to solve a benchmark problem of distillation column robust control design.