Robust control design for time-delay systems using non-causal uncertainty blocks

Robust controller design problem for time-delay systems is considered. Both the time-delays, which may appear at the inputs and/or outputs of the plant, and the finite-dimensional part of the plant are assumed to be subject to uncertainties. A recent result, which utilizes non-causal blocks to represent the uncertainties in the time-delays, is extended to the present case. A number of different representations are considered for the uncertainties in the finite-dimensional part of the plant. For each of these representations, it is shown that the time-advances in the uncertainty blocks have a special form. This special form with the newly introduced strong small-gain conditions allow the design of an ℋ_∞-optimal controller for the present problem.