On vanishing stability regions in nonlinear systems with high-gain feedback

When local stabilization of nonlinear systems is achieved by linear feedback, the resulting stability region may vanish as the feedback gains increase. This is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium. As the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium. If a feedback linearization design is applied, the same instability mechanism may occur when the nonlinearities are not precisely known.