In the last decade the so-called
model reduction has received much attention becoming an important research topic in applied mathematics. Basically the reduction problem involves approximating a stable system with
states by another stable system with
states such that the associated model error satisfies a prescribed
norm bound constraint. Most of the results have been derived in the context of continuous and discrete-time systems without delays and parameter uncertainties. The main aim of the present paper consists in studying the problem of
model reduction for linear continuous time-delay systems. The case including systems with parameter uncertainties is analysed separately. In this respect, sufficient conditions based upon linear matrix inequalities and a coupling non-convex rank constraint are proposed in order to assure the existence of the desired reduced-order model. A simple illustrative example is also given to show the effectiveness of the proposed approach.