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Regions of Attraction

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Control of Complex Systems

Part of the book series: Communications and Control Engineering ((CCE))

Abstract

In dealing with nonlinear systems whose equilibria are locally stable, it is critically important to have a reliable method for estimating the region of attraction. Developing efficient algorithms for this purpose is not an easy task, particularly when the system is large. One of the main challenges in this context is to keep the overall computation time and the associated memory requirements within acceptable limits. An additional (and equally important) objective is to enlarge the size of the estimate by an appropriate choice of feedback. In the case of large-scale systems, this choice is usually restricted to some form of decentralized control, since state information is available only locally.

Most of the existing methods for estimating the region of attraction are based on Lyapunov’s theory and its various extensions (such as La Salle’s invariance principle, for example). The main difficulty with this approach lies in its conservativeness, which is reflected by the fact that the obtained estimates usually represent only a subset of the exact region. This problem has been the subject of extensive research over the past few decades, and a number of possible improvements have been proposed (see e.g., Weissenberger, 1973; Šiljak, 1978; Genesio et al., 1985; Zaborszky et al., 1988; Levin, 1994; Chiang and Fekih- Ahmed, 1996; Rodrigues et al., 2000; Khalil, 2001; Gruyitch, et al., 2003; Tan and Packard, 2008; Chesi, 2009).

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Authors and Affiliations

  1. Dept. Electrical Engineering, Santa Clara University, 500 EI Camino Real, Santa Clara, CA, 95053, USA

    Aleksandar I. Zečević & Dragoslav D. Šiljak

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  1. Aleksandar I. Zečević
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  2. Dragoslav D. Šiljak
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Correspondence to Aleksandar I. Zečević .

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Zečević, A.I., Šiljak, D.D. (2010). Regions of Attraction. In: Control of Complex Systems. Communications and Control Engineering. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1216-9_4

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  • DOI: https://doi.org/10.1007/978-1-4419-1216-9_4

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