Robust stability and instability of nonlinear feedback system with uncertainty-dependent equilibrium

In this paper, we consider robust stability and instability of an uncertain nonlinear system with an uncertainty-dependent equilibrium. In conventional approaches to the analysis, it is assumed that the location of the equilibrium in the nonlinear system is not shifted by the uncertainty and then the robustness is discussed. However, the assumption does not hold for general nonlinear systems. We consider nonlinear feedback systems with dynamic uncertainties and propose robust stability and instability analysis methods for such systems by treating the uncertainty-dependent equilibrium. Finally, an illustrative example for stability and instability analysis of an uncertain genetic network model is presented.