H∞ /H2 model reduction through dilated linear matrix inequalities

This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field{N}$. Arbitrary order of the reduced model can be enforced by including states in the original system with negligible input-to-output system norms. The use of dilated LMI conditions facilitates model reduction of parameter-dependent systems. When a reduced model determined by the sufficient LMI conditions does not satisfactorily approximates the original system, an iterative algorithm based on dilated LMIs is proposed to significantly improve the approximation bound. The effectiveness of the method is accessed by numerical experiments. The method is also applied to the $H_2$ order reduction of a flexible wind turbine model.