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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 467629, 17 pages
http://dx.doi.org/10.1155/2012/467629
Research Article

Stability of Teleoperation Systems for Time-Varying Delays by Neutral LMI Techniques

1Higher Technical School of Industrial Engineering, University of Vigo, 36310 Vigo, Spain
2Higher Technical School of Computer Engineering, University of Vigo, 32004 Orense, Spain

Received 26 June 2012; Revised 18 October 2012; Accepted 22 October 2012

Academic Editor: Alexander Pogromsky

Copyright © 2012 Emma Delgado et al. 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

This paper investigates the delay-dependent stability of a teleoperation system based on the transparent Generalized Four-Channel control (G-4C) scheme under time-varying communication delays. To address stability we choose here a primitive result providing a Linear Matrix Inequalities (LMIs) approach based on Lyapunov-Krasovskii functionals. Firstly, the scheme is modeled as the neutral-type differential-delayed equation; that is, the delay affects not only the state but also the state derivative. Secondly, we apply a less conservative stability criteria based on LMIs that are delay dependent and delay's time-derivative dependent. The reason is that, for better performance in the case of small delays, we must accept the possibility that stability is lost for large delays. The approach is applied to an example, and its advantages are discussed. As a result, we propose to modify the values of standard controllers in G-4C defining the -4C scheme, which introduces a tuning factor to increase in practical conditions the stable region fixing the desired bounds on time-varying delay, with the particularity of maintaining the tracking properties provided by this transparent control scheme. The simulation results justify the proposed control architecture and confirm robust stability and performance.