Time-delay dependent H∞ model reduction for uncertain stochastic systems: Continuous-time case

The problem of robust H∞ model reduction for uncertain stochastic systems with time delay is investigated in this paper. The attention of this paper is focused on the construction of a reduced-order model for a given stable system. Several sufficient conditions are obtained for ensuring the existence of the reduced-order model by means of linear matrix inequalities and a coupling non-convex rank con-straint condition. Under the sufficient conditions, the desired reduced-order model can be constructed, and the error system between the original model and the reducedorder model is asymptotically stable and has a prescribed H∞ performance. Based on the proposed method, the construction approaches of reduced-order models with special structures, such as the zeroth-order model, the delay-free model, and the noparameter-uncertainties model, are also developed. Finally, the effectiveness of the proposed model reduction method is illustrated by a numerical simulation example.