Achieving nonvanishing stability regions with high-gain cheap control using H/sup /spl infin// techniques: the second order case

We use asymptotically optimal H/sup /spl infin// design techniques to develop a high-gain linear feedback controller to stabilize a class of nonlinear systems. We determine conditions on the design parameters to guarantee that the high-gain control does not cause the stability region to vanish. Our approach uses a Lyapunov function to derive a sufficient condition to maintain the stability region for a second-order system when we know a bound on the nonlinear terms. A simulation confirms the results.