Robust Constrained Regulator Problem for Linear Uncertain Systems

Abstract

The robust regulator problem for linear uncertain systems with constrained control is considered. Necessary and su.cient conditions of positive invariance of polyhedral domains with respect to motion of uncertain systems are given. Further, it is shown that in contrast to the case of perfectly known systems, positive invariance with respect to uncertain systems and stability of n - m assigned eigenvalues from the open loop system do not imply asymptotic stability. Furthermore, conditions ensuring this asymptotic stability are derived. This enables us to construct robust constrained regulators, i.e., control laws satisfying control constraints and achieving asymptotic stability in presence of parametric uncertainties.