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We present quadratically convergent algorithms to compute the extremal valueof a real parameter for which a given rational transfer function of a lineartime-invariant system is passive. This problem is formulated for bothcontinuous-time and discrete-time systems and is linked to the problem offinding a realization of a rational transfer function such that its passivityradius is maximized. Our new methods make use of the HybridExpansion-Contraction algorithm, which we extend and generalize to the settingof what we call root-max problems.

Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems