Péter Polcz(1*), Gábor Szederkényi(2)

(1) Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/A, Budapest, 1083, HUNGARY
(2) Systems and Control Lab, Institute for Computer Science and Control, Hungarian Academy of Sciences, Práter u. 50/A., Budapest, 1083, HUNGARY
(*) Corresponding Author

Computational Stability Analysis of Lotka-Volterra Systems


Abstract



This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV) systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4) dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.

Keywords


nonlinear systems; Lotka-Volterra models; stability analysis; linear matrix inequalities; Lyapunov function

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