Generalization of all stabilizing compensators for finite-dimensional linear systems

Abstract

For finite-dimensional linear systems, the Youla-Kucera parameterization (YKP) with a Q parameter over RH infinity is assumed to satisfy the Diophantine identity. However, the stability is guaranteed if the Diophantine equation is the "U(RH infinity)" equality, but not if it is the "identity" equality. However, Vidyasagar's structure with an H parameter over U(RH infinity) is an observer-controller configuration that satisfies the Diophantine equation. This study discusses the deficiency of the Diophantine identity; expands the YKP using an H parameter over U(RH infinity), and expands the Vidyasagar's structure using a Q(v) parameter over RH infinity so that both of the expanded parameterizations satisfy the Diophantine equation and are equivalent for all stabilizing compensators. Moreover, an equation that relates to Q, Q(v), and H will be introduced to establish relationships among the YKP, Vidyasagar's structure and both expanded parameterizations. (c) 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.