A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems

Abstract

Citation for published version (APA):Böhm, C., Lazar, M., & Allgöwer, F. (2010). A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems. In Proc. 49th IEEE Conference on Decision and Control (CDC), 15-17 December 2010, Atlanta, Georgia (pp. 3277-3282 Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at:openaccess@tue.nl providing details and we will investigate your claim. Abstract-This paper proposes a novel approach to stability analysis and controller synthesis for discrete-time periodically time-varying systems. Firstly, a relaxation of standard Lyapunov conditions is derived. This leads to a less conservative Lyapunov function that is required to decrease at every period, rather than at each time instant. Secondly, several solutions for synthesizing such periodic control Lyapunov functions are presented. These solutions make use of on-line optimization and can be formulated as a semi-definite program for constrained linear periodic systems. An example illustrates the effectiveness of the developed method.

A new methodology to compute stabilizing control laws for continuous‐time LTV systems

“…Concerning specifically Corollary , the main motivation for treating the stabilization problem by solving a set of periodic discrete‐time systems is that there exist, in the literature, several papers devoted to such systems. Therefore, the corollary significantly enhances the proposed synthesis methodology by allowing the utilization of a considerably higher number of stabilization techniques (see, for example, other works). In the following, the adaptation of the periodic discrete‐time technique presented in the work of de Souza and Trofino to generate a stabilizing continuous‐time state‐feedback gain is presented.…”