Analysis of the stability of the two-dimensional Lotka-Volterra mutual system

In this article, a robust positive control is proposed to estabilize a family of nonlinear positive systems. Sufficient conditions are provided for stabilization by sliding modes, which entails the robustness of the feedback system. The construction of a stabilizing line with sliding dynamics is detailed. The feasibility of the stabilization method is illustrated by studying a twodimensional Lotka-Volterra mutualistic system where the sliding conditions, the construction of the segment of the stabilizing line and the robustness of the bounded positive control are shown.