Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2008, Article ID 732039, 20 pages doi:10.1155/2008/732039 Research Article Bounding the Output Error in a Buck Power Converter Using Perturbation Theory Fabiola Angulo, 1 Enric Fossas, 2 Tere M. Seara, 3 and Gerard Olivar 1 1 Departamento de Ingenier´ ıa El´ ectrica, Electr´ onica y Computaci´ on, Universidad Nacional de Colombia, Cra 27 No. 64-60 Manizales, Caldas, Colombia 2 Institute of Industrial and Control Engineering, Technical University of Catalonia, 08028 Barcelona, Spain 3 Departamento de Matem` atica Aplicada IV, Universitat Polit` ecnica de Catalunya, 08034 Barcelona, Spain Correspondence should be addressed to Gerard Olivar, golivart@unal.edu.co Received 20 January 2008; Revised 30 May 2008; Accepted 20 July 2008 Recommended by Oleg Gendelman We show the main results obtained when applying the average theory to Zero Average Dynamic control technique in a buck power converter with pulse-width modulation PWM. In particular, we have obtained the bound values for output error and sliding surface. The PWM with centered and lateral pulse configurations were analyzed. The analytical results have confirmed the numerical and experimental results already obtained in previous publications. Moreover, through an important lemma, we have generalized the theory for any stable second-order system with relative degree 2, using properties related to transformations and stability of linear systems. Copyright q 2008 Fabiola Angulo 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. 1. Introduction Switching sources are devices used in the implementation of power converters. As a consequence of the switching action, chattering, high-order harmonic distortion, and nonlinear phenomena appear. The latter can be dealt with control techniques 1, while chattering and harmonic distortion, inherent to switching, can be reduced, but not avoided, using fixed switching frequency. To achieve this reduction, some techniques have been reported: adaptive hysteresis band 2, 3, signal injection with a selected frequency 3–7, zero average current in each iteration ZACE8, and recently zero average error dynamics in each iteration ZAD9. ZAD control scheme, proposed in 9, adds the advantages of fixed frequency implementations and the inherent robustness of sliding control modes. It is based on an appropriate design of the duty cycle in such a way that the sliding surface average in each