PEDS: Passivity enforcement for descriptor systems via Hamiltonian-symplectic matrix pencil perturbation

Abstract

Passivity is a crucial property of macromodels to guarantee stable global (interconnected) simulation. However, weakly nonpassive models may be generated for passive circuits and systems in various contexts, such as data fitting, model order reduction (MOR) and electromagnetic (EM) macromodeling. Therefore, a post-processing passivity enforcement algorithm is desired. Most existing algorithms are designed to handle pole-residue models. The few algorithms for state space models only handle regular systems (RSs) with a nonsingular D+DT term. To the authors' best knowledge, no algorithm has been proposed to enforce passivity for more general descriptor systems (DSs) and state space models with singular D+DT terms. In this paper, a new post-processing passivity enforcement algorithm based on perturbation of Hamiltonian-symplectic matrix pencil, PEDS, is proposed. PEDS, for the first time, can enforce passivity for DSs. It can also handle all kinds of state space models (both RSs and DSs) with singular D+DT terms. Moreover, a criterion to control the error of perturbation is devised, with which the optimal passive models with the best accuracy can be obtained. Numerical examples then verify that PEDS is efficient, robust and relatively cheap for passivity enforcement of DSs with mild passivity violations.