Robust stabilization of uncertain systems by periodic feedback

Abstract

An uncertain control system described by a family parametrized by an unknown parameter that takes values in a known constraint set is considered. The robust stabilization problem is defined as finding a dynamic output controller that globally stabilizes the uncertain system; that is, no matter what the parameter value chosen by ‘Nature’, the closed-loop system is globally asymptotically stable. It is shown that in the class of dynamic periodic controllers the solution to this problem exists under reasonable assumptions given for a general family of abstract non-linear models. Those assumptions, in the case of a family of linear finite-dimensional models, are equivalent to suitable stabilizability and detectability assumptions. For this case, insensitivity of the design with respect to small errors in the data is proved.