Robust L1 model reduction for time-delay systems

This paper investigates the problem of robust L-1 model reduction for linear continuous time-delay systems with parameter uncertainties. For a given stable system, our purpose is to construct reduced-order systems, such that the error system between the two models is asymptotically stable and has a guaranteed L-1 performance constraint. The L-1 performance criterion is first established for time-delay systems, furthermore, the sufficient conditions for the existence of admissible reduced-order models are obtained in terms of linear matrix inequalities (LMI) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) algorithm is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by the standard numerical software. In addition, the development of delay-free reduced-order models is also presented. The efficiency of the proposed technique is demonstrated by a numerical example.