The trade-off between H∞ attenuation and uncertainty tolerance by quasiconvex optimization

Uncertainty tolerance and H_∞ attenuations are two important concerns in feedback control design. It is therefore important to develop effective methods to compute the trade-off between these two objectives. Using quasiconvex optimization approach, this paper develops algorithms for two problems in this regard: 1) given the uncertainty size of the system, compute the minimum H_∞ norm bound of the closed loop system reachable by state feedback control; and 2) given the required maximum acceptable H_∞ norm bound of the closed loop system, compute the maximum uncertainty size which can be tolerated when state feedback control is applied. A numerical example is included to show the trade-off between uncertainty tolerance and H_∞ attenuations, and the effectiveness of the algorithms.