Robust 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_∞ state-feedback control for retarded systems is applied. The theory is used to solve a benchmark problem of distillation column robust control design.