Open AccessPassivity of Lotka–Volterra and quasi-polynomial systems
Author(s) -
Lőrinc Márton,
Katalin M. Hangos,
Attila Magyar
Publication year - 2021
Publication title -
nonlinearity
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.571
H-Index - 90
eISSN - 1361-6544
pISSN - 0951-7715
DOI - 10.1088/1361-6544/abd52b
Subject(s) - passivity , control theory (sociology) , mathematics , polynomial , exponential stability , stability (learning theory) , controller (irrigation) , full state feedback , state (computer science) , computer science , control (management) , nonlinear system , mathematical analysis , engineering , algorithm , agronomy , physics , quantum mechanics , artificial intelligence , machine learning , electrical engineering , biology
This study approaches the stability analysis and controller design of Lotka–Volterra and quasi-polynomial systems from the perspective of passivity theory. The passivity based approach requires to extend the autonomous system model with a suitable input structure. The condition of passivity for Lotka–Volterra systems is less strict than the classic asymptotic stability criterion. It is shown that each Lotka–Volterra system is feedback equivalent to a passive system and a passifying state feedback controller is proposed. The passivity based approach enables the design of novel state feedback controllers to Lotka–Volterra systems. The asymptotic stability can be achieved by applying an additional diagonal state feedback having arbitrarily small gains. This result was further explored to achieve rate disturbance attenuation in controlled Lotka–Volterra systems. By exploiting the dynamical similarities between the Lotka–Volterra and quasi-polynomial systems, it was shown that the passivity related results, developed for Lotka–Volterra systems, are also valid for a large class of quasi-polynomial systems. The methods and tools developed have been illustrated through simulation case studies.