2016/04/04 by Giórgio Valmórbida, James Anderson, Valmorbida, Giorgio +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1604.01084
openalex publication_date 2016/04/04 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
This work addresses the problem of estimating the region of attraction (RA)\nof equilibrium points of nonlinear dynamical systems. The estimates we provide\nare given by positively invariant sets which are not necessarily defined by\nlevel sets of a Lyapunov function. Moreover, we present conditions for the\nexistence of Lyapunov functions linked to the positively invariant set\nformulation we propose. Connections to fundamental results on estimates of the\nRA are presented and support the search of Lyapunov functions of a rational\nnature. We then restrict our attention to systems governed by polynomial vector\nfields and provide an algorithm that is guaranteed to enlarge the estimate of\nthe RA at each iteration.\n