2021/09/02 by Timothy J. Mitchell, Paul Van Dooren, Mitchell, Tim +1
Engineering · Mathematics · #37J25 #49M15 #93C05 #93D09 #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2109.00974
openalex publication_date 2021/09/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.