Global stability of uncertain rational nonlinear systems with some positive states

This paper presents LMI conditions for local and global asymptotic stability of rational uncertain nonlinear systems where some or all the state variables are constrained by the model to have definite signal. The uncertainties are modeled as real time varying parameters with magnitude and rate of variation bounded by given polytopes. The stability conditions are based on a rational Lyapunov function with respect to the states and uncertain parameters. A numerical example is used to illustrate the potential of the proposed results.