We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is passive. This problem is formulated for both continuous-time and discrete-time systems and is linked to the problem of finding a realization of a rational transfer function such that its passivity radius is maximized. Our new methods make use of the Hybrid Expansion-Contraction algorithm, which we extend and generalize to the setting of what we call root-max problems.

翻译：我们提出二次趋同算法,以计算一个真实参数的极限值,对于这个参数,线性时间变量系统的某种合理转移功能是被动的。这个问题是为连续时间和离散时间系统而设计的,与找到一个合理转移功能以实现的问题有关,从而使其被动半径最大化。我们的新方法利用混合扩展-订约算法,我们将其扩展和概括到我们称之为根轴问题的设置上。