Matrix nearness-based guaranteed passive system approximation

In this paper we present a new approach towards global passive approximation in order to find a passive real-rational transfer function G ( s ) that is an arbitrarily close approximation of the passive transfer function nearest to a non-passive square transfer function H ( s ) . It is based on existing solutions to pertinent matrix nearness problems. It is shown that the key point in constructing the passive real-rational transfer function G ( s ) , is to find a good rational approximation of the well-known ramp function over an interval defined by the minimum and maximum dissipation of H ( s ) . The proposed algorithms rely on the stable–anti-stable decomposition of a given transfer function. Pertinent examples are given to show the scope and accuracy of the proposed algorithms.