Global passive system approximation

TL;DR

This paper introduces a novel method for globally approximating non-passive transfer functions with passive ones by leveraging matrix nearness problems and rational approximation of the ramp function, ensuring minimal deviation in a matrix norm.

Contribution

It presents a new algorithm for passive approximation that uses rational approximation of the ramp function and stable anti-stable projection techniques.

Findings

Algorithms effectively approximate non-passive transfer functions with passive ones.

The method achieves high accuracy in examples demonstrating scope and effectiveness.

The approach is grounded in matrix nearness problems and rational approximation theory.

Abstract

In this paper we present a new approach towards global passive approximation in order to find a passive transfer function G(s) that is nearest in some well-defined matrix norm sense to a non-passive 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 nearest passive transfer function, 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 projection of a given transfer function. Pertinent examples are given to show the scope and accuracy of the proposed algorithms.