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

A new model order reduction technique is presented which preserves passivity and non-expansivity. It is a projection-based method which exploits the solution of linear matrix inequalities 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 linear matrix inequality can be replaced by equivalently solving an algebraic Riccati equation, which is known to be a more efficient approach. A new algebraic Riccati equation 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. Three pertinent examples comparing the present approach with positive-real balanced truncation show the strength and accuracy of the present approach.