Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 817063, 26 pages
Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding
1Department of Electricity and Electronics, Institute of Research and Development of Processes (IIDP), Faculty of Science and Technology, University of the Basque Country, Leioa (Bizkaia), P.O. Box 644, 48080 Bilbao, Spain
2Department of Automatic Control and Systems Engineering, College of Industrial Technical
Engineering (EUITI) Bilbao, University of the Basque Country, Bilbao (Bizkaia), Plaza de la Casilla 3, 48012 Bilbao, Spain
3Department of Applied Mathematics, College of Industrial Technical Engineering (EUITI) Bilbao, University of the Basque Country, Bilbao (Bizkaia), Plaza de la Casilla 3, 48012 Bilbao, Spain
Received 3 November 2006; Revised 20 July 2007; Accepted 19 December 2007
Academic Editor: Angelo Luongo
Copyright © 2008 M. de la Sen 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.
This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.