Model order reduction with preservation of passivity, non-expansivity and Markov moments

A new model order reduction (MOR) technique is presented which preserves passivity and non-expansivity. It is a projection-based method which exploits the solution of Linear Matrix Inequalities (LMI’s) to generate a descriptor state space format which preserves positive-realness and bounded-realness. In the case of both non-singular and singular systems, solving the LMI can be replaced by equivalently solving an algebraic Riccati equation (ARE), which is known to be a more efficient approach. A new ARE and a frequency inversion technique are also presented to specifically deal with the important singular case. The preservation of Markov moments is also guaranteed by the judicious choice of a projection matrix.