Lu, Pingli; Yang, Ying; Li, Zhongkui; Huang, Lin Decentralized dynamic output feedback for globally asymptotic stabilization of a class of dynamic networks. (English) Zbl 1152.93302 Int. J. Control 81, No. 7, 1054-1061 (2008). Summary: The objective of this paper is to propose an approach to stabilization of a class of dynamic networks with each node being a non-linear system with multiple equilibria. The proposed algorithms, which are developed within the convex optimization framework, employ a decentralized dynamic output feedback structure. Furthermore, an interesting conclusion is reached, in which the stabilization problem for the whole \(N\)n-dimensional dynamic networks can be converted into the simple \(n\)-dimensional space in terms of only three LMIs. An application of output stabilization of mutually coupled phase-locked loop networks is used to verify the effectiveness of the proposed methods. Cited in 3 Documents MSC: 93A14 Decentralized systems 93D15 Stabilization of systems by feedback 93D20 Asymptotic stability in control theory PDFBibTeX XMLCite \textit{P. Lu} et al., Int. J. Control 81, No. 7, 1054--1061 (2008; Zbl 1152.93302) Full Text: DOI References: [1] DOI: 10.1109/26.64662 · doi:10.1109/26.64662 [2] DOI: 10.1109/TAC.2002.806652 · Zbl 1364.90244 · doi:10.1109/TAC.2002.806652 [3] Buckwalter J, IEEE Radio Freq. Integ. Circ. Symp. pp 181– (2000) [4] DOI: 10.1016/j.automatica.2006.06.004 · Zbl 1130.93422 · doi:10.1016/j.automatica.2006.06.004 [5] DOI: 10.1016/j.automatica.2007.02.003 · Zbl 1128.93313 · doi:10.1016/j.automatica.2007.02.003 [6] Gahinet, P, Nemirovski, A, Laub, AJ and Chilali, M. May 1995.LMI Control Toolbox User’s Guide, May, 01760–1500. Natick, Mass: The Math-Works, Inc. 24 Prime Park Way [7] DOI: 10.1016/S0960-0779(03)00197-8 · Zbl 1085.93514 · doi:10.1016/S0960-0779(03)00197-8 [8] DOI: 10.1016/0005-1098(94)90110-4 · Zbl 0806.93017 · doi:10.1016/0005-1098(94)90110-4 [9] DOI: 10.1109/9.887638 · Zbl 0989.93008 · doi:10.1109/9.887638 [10] DOI: 10.1080/00207170010025258 · Zbl 1015.93058 · doi:10.1080/00207170010025258 [11] Leonov GA, Frequency Methods in Oscillation Theory (1992) [12] Leonov GA, Non-local Methods for Pendulum-like Feedback Systems (1992) [13] DOI: 10.1142/9789812798695 · doi:10.1142/9789812798695 [14] DOI: 10.1109/TCSI.2004.835655 · Zbl 1374.94915 · doi:10.1109/TCSI.2004.835655 [15] DOI: 10.1142/S0218127402004292 · doi:10.1142/S0218127402004292 [16] DOI: 10.1016/j.physa.2007.03.026 · doi:10.1016/j.physa.2007.03.026 [17] DOI: 10.1016/j.physa.2007.05.030 · doi:10.1016/j.physa.2007.05.030 [18] DOI: 10.1016/j.physa.2003.10.052 · doi:10.1016/j.physa.2003.10.052 [19] Lu PL, Nonlinear Analysis (2007) [20] Lu PL, Nonlinear Analysis (2007) [21] DOI: 10.1016/0167-6911(95)00063-1 · Zbl 0866.93052 · doi:10.1016/0167-6911(95)00063-1 [22] DOI: 10.1109/81.974874 · Zbl 1368.93576 · doi:10.1109/81.974874 [23] DOI: 10.1142/S0218127402004292 · doi:10.1142/S0218127402004292 [24] DOI: 10.1016/j.sysconle.2006.10.001 · Zbl 1108.93051 · doi:10.1016/j.sysconle.2006.10.001 [25] DOI: 10.1109/4.44991 · doi:10.1109/4.44991 [26] Yakubovich VA, Stability of Stationary Sets in Control Systems with Discontinous nonlinearities (2004) · doi:10.1142/5442 [27] DOI: 10.1016/j.sysconle.2004.02.024 · Zbl 1157.93382 · doi:10.1016/j.sysconle.2004.02.024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.