Efficient Localization Methods for Passivity Enforcement of Linear Dynamical Models

Abstract

This paper describes a novel approach for passivity enforcement of compact dynamical models of electrical interconnects. The proposed approach is based on a parameterization of general state-space scattering models with fixed poles. We formulate the passivity constraints as a unitary boundedness condition on the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm of the system transfer function. When this condition is not verified, we use it as an explicit constraint within an iterative perturbation loop of the system state-space matrices. Since the resulting optimization framework is convex but nonsmooth, we solve it via localization based algorithms, such as the ellipsoid and the cutting plane methods. The proposed technique solves two critical bottleneck issues of the existing approaches for passivity enforcement of linear macromodels. Compared to quasi-optimal schemes based on singular value or Hamiltonian eigenvalue perturbation, we are able to guarantee convergence to the optimal solution. Compared to convex formulations based on direct Bounded Real Lemma constraints, we are able to reduce both memory and time requirements by orders of magnitude. We demonstrate the effectiveness of our approach on a number of cases for which existing algorithms either fail or exhibit very slow convergence.