Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 132597, 16 pages
Research Article

Stabilization of Time-Varying System by Controllers with Internal Loop

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 18 April 2012; Accepted 10 May 2012

Academic Editor: Zidong Wang

Copyright © 2012 Yufeng Lu and Chengkai Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the concept of stabilization with internal loop for infinite-dimensional discrete time-varying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the controller with internal loop overcomes the awkwardness brought by the extra invertibility condition in the parametrization of the conventional controllers. We also prove that the strong stabilization problem can be completely solved in the closed-loop system with internal loop. Thus the advantage of the controller with internal loop is addressed in the framework of nest algebra.