A separation principle for robust stabilization of linear systems

Abstract

The well-known separation principle plays a vital role in output feedback control of linear systems. The lack of a suitable separation principle for uncertain linear systems makes output feedback control for these systems a challenging problem. This paper is concerned with the problem of robust output feedback stabilization for a class of uncertain linear systems admitting the so-called stepwise augmentation structure. This structure is generated via a sequence of up and down augmentations, including the well-known lower and upper triangular structures as special cases. We provide a recursive, state-space design approach for constructing quadratically stabilizing output feedback controllers. This design approach is based on a new separation principle for uncertain linear systems, which we believe is a powerful tool for robust control.