Global Stabilization of Lotka–Volterra Systems With Interval Uncertainty.

This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka–Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all other vertices, which makes it easier to check the stability of the whole uncertain system. A subtle use of this fact in stabilization of interval LV systems via FLSF leads to a sufficient condition in terms of linear matrix inequalities. Also, the proposed approach is extended to a wider class of LV systems with time-varying and state-dependent system matrices. The efficiency of the proposed scheme is shown through numerical examples and simulations. [ABSTRACT FROM AUTHOR]