2020/12/04 by Corbin Klett, Matthew Abate, Klett, Corbin +5
Biochemistry, Genetics and Molecular Biology · Engineering · #Control Systems and Identification #FOS: Electrical engineering #Gene Regulatory Network Analysis #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2012.02874
openalex publication_date 2020/12/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Stability margins for linear time-varying (LTV) and switched-linear systems\nare traditionally computed via quadratic Lyapunov functions, and these\nfunctions certify the stability of the system under study. In this work, we\nshow how the more general class of homogeneous polynomial Lyapunov functions is\nused to compute stability margins with reduced conservatism, and we show how\nthese Lyapunov functions aid in the search for periodic trajectories for\nmarginally stable LTV systems. Our work is premised on the recent observation\nthat the search for a homogeneous polynomial Lyapunov function for some LTV\nsystems is easily encoded as the search for a quadratic Lyapunov function for a\nrelated LTV system, and our main contribution is an intuitive algorithm for\ngenerating upper and lower bounds on the system's stability margin. We show\nalso how the worst-case switching scheme - which draws an LTV system closest to\na periodic orbit - is generated. Three numerical examples are provided to aid\nthe reader and demonstrate the theoretical contributions of the work.\n