Nonfragile controllers for rejection of exogenous disturbances

We consider design of stabilizing controllers for linear systems subjected to persistent exogenous disturbances. The performance index for the closed-loop system is taken in the form of the “size” of the invariant (bounding) ellipsoid for its output. The optimal controller that attains the minimal size is shown to be fragile in the sense that small variations of its coefficients lead to a dramatic degradation of the quality or even to the loss of stability. We show how to design a nonfragile stabilizing controller that tolerates variations of its parameters and yields much smaller ellipsoids. The approach is exemplified through a well-known benchmark control problem for a mechanical two-mass-spring system.