Achieving nonvanishing stability regions with high-gain cheap control using H-infinity techniques: the second-order case

This paper demonstrates how to use an asymptotically H-infinity-optimal con troller to stabilize a second-order system subject to unknown disturbances such that the stability region does not vanish as the feedback gains increa se. The high-gain feedback arises when one attempts to achieve the lowest a chievable limit of the disturbance attenuation Linder the H-infinity-design . This type of gain increase can cause the stability region to vanish if th e disturbance contains nonlinear terms. The analysis using Lyapunov techniq ues derives a sufficient condition on the design parameters to prevent the stability region from vanishing. In addition to describing exact solutions for six different cases, the paper provides simulations to illustrate the r esults. (C) 2001 Elsevier Science B.V. All rights reserved.