On Stability and Trajectory Boundedness of Lotka–Volterra Systems With Polytopic Uncertainty

Abstract

A new approach is proposed to study the stability property of the feasible equilibrium point and the trajectory boundedness of the Lotka-Volterra (LV) dynamics in the presence of polytopic uncertainties. Stability analysis of general LV systems is not straightforward in comparison with its cooperative counterpart. It is shown that, under specific conditions, the trajectory of the cooperative counterpart of the LV system can be considered as an upper bound for the trajectory of the corresponding dynamics. Consequently, the stability of the cooperative counterpart of the LV system leads to boundedness of the trajectory. The obtained results are extended for the LV systems with polytopic uncertainties. It is shown that under specific conditions, there is a region which the trajectory of the system belongs to it as time tends to infinity. Also, the stability of LV systems with polytopic uncertainty is investigated. The obtained results are confirmed through some numerical/application-based examples.