H∞ output feedback control for delay systems with nonlinear and parametric uncertainties

Robust H_∞ output feedback control is considered for linear systems with multiple time-varying delays and with nonlinear and parametric uncertainties in the state, input and measurement output, appearing in all system matrices. Firstly, some new sufficient conditions in the form of the GBRL (generalised bounded real lemma) are derived, which are more convenient to deal with controller design problems for uncertain delay systems in the LMI framework. A new solvability condition is presented to design an H_∞ output feedback controller for systems without uncertainties, but with multiple time-delays in the state, the input and the output, which also generalises some previous results for control problems of delay systems. Then the results are extended to time-delay systems with nonlinear uncertainties and are finally generalised to delay systems with both nonlinear and parametric uncertainties in linear fractional form involving all system matrices. The robust H_∞ output feedback controllers can be constructed based on the LMI approach and correspondingly the solvability of these robust control problems for uncertain delay systems can be reduced to that for an auxiliary system without any uncertainty. Numerical examples are provided to demonstrate the methods