Riccati Equations, Network Theory and Brune Synthesis: Old Solutions for Contemporary Problems

Abstract

Riccati equations have a natural connection with network theory. Classical passive network synthesis procedures, employing often frequency domain spectral factorization, can be mirrored by state variable procedures which rely on knowledge of a steady state Riccati equation solution. In contrast to many occurrences of steady state Riccati equations, it is possible (especially in network applications) to encounter equations which have strong, but not stabilizing solutions. Such equations constitute a problem for much software. Classical network synthesis procedures actually dealt with a frequency domain version of this problem using tools such as the Brune synthesis. The Riccati equation equivalent involves a deflation technique which will be exposed.

The authors acknowledge funding of activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program, funding of this research by the US Army Research Office, Far East, the Office of Naval Research, Washington.