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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 612198, 17 pages
http://dx.doi.org/10.1155/2012/612198
Research Article

Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Campus de Leioa (Bizkaia), P.O. Box 644 de Bilbao, 48080 Bilbao, Spain

Received 13 August 2012; Accepted 17 October 2012

Academic Editor: Haydar Akca

Copyright © 2012 M. De la Sen. 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.

Abstract

The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs on a Hilbert space of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.