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Kuhn-Tucker-based stability conditions for systems with saturation

Primbs, James A. and Gianelli, Monica (2001) Kuhn-Tucker-based stability conditions for systems with saturation. IEEE Transactions on Automatic Control, 46 (10). pp. 1643-1647. ISSN 0018-9286. https://resolver.caltech.edu/CaltechAUTHORS:PRIieeetac01

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Abstract

This paper presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented can be extended to handle a dead-zone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities, which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods.


Item Type:Article
Additional Information:© 2001 IEEE. Reprinted with permission. Manuscript received April 29, 2000; revised December 7, 2000 and March 5, 2001. Recommended by Associate Editor T. Iwasaki. The authors would like to acknowledge helpful discussions with A. Jadbabaie and P. Parrilo.
Subject Keywords:Kuhn–Tucker conditions, linear system, Lyapunov function, S-procedure, saturation
Issue or Number:10
Record Number:CaltechAUTHORS:PRIieeetac01
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:PRIieeetac01
Alternative URL:http://dx.doi.org/10.1109/9.956065
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1441
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Jan 2006
Last Modified:02 Oct 2019 22:43

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