Invariance and nonfragility in the rejection of exogenous disturbances

In this paper we consider design of stabilizing controllers for linear systems subjected to persistent exogenous disturbances. The performance of the closed-loop system is characterized by the size of invariant (bounding) ellipsoid for the system state (output). The optimal (smallest) ellipsoid is shown to be “fragile” in the sense that small variations of its coefficients may lead to considerable degradation of performance or even to the loss of stability of the closed-loop system. We propose a method for constructing a “nonfragile” controller that tolerates variations of the parameters and remains optimal in the sense of the performance index adopted.