Robustness measure bounds for Lyapunov-type state-feedback systems

The theorems introduced by Patel (1977) for multivariable linear-quadratic (LQ) state-feedback designs in the presence of perturbations are extended to Lyapunov-type state-feedback designs. A robustness measure bound is introduced for Lyapunov-type state-feedback systems. Bounds are obtained for allowable nonlinear time-varying perturbations, so that the resulting closed-loop system remains stable. Bounds on a special, but important, class of perturbations, in which the perturbation is linear, are also derived.