On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian
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Cites background from "On maximizing the second smallest e..."
...This includes subjects such as consensus [47, 9, 5, 15, 54, 8, 79], collective behavior of flocks and swarms [66, 80, 60, 95, 30], sensor fusion [64, 71, 33], random networks [34, 73], synchronization of coupled oscillators [81, 39, 72, 73, 14], algebraic connectivity(6)of complex networks [65, 12, 43], asynchronous distributed algorithms [54, 26], formation control for multi-robot systems [21, 68, 69, 24, 89, 88, 48, 96, 20], optimization-based cooperative control [75, 42, 37, 2], dynamic graphs [56, 61, 40, 99], complexity of coordinated tasks [36, 44, 52, 53], and consensus-based belief propagation in Bayesian networks [78, 67]....
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3,028 citations
Cites background from "On maximizing the second smallest e..."
...A related problem is considered in [48], where an iterative, semidefinite-programming-based approach is developed to maximize the algebraic connectivity of the Laplacian of undirected graphs (see “A Tutorial on Graph Theory”) with the motivation that the algebraic connectivity of the Laplacian characterizes the convergence rate of the consensus algorithm....
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Cites background from "On maximizing the second smallest e..."
...Boyd (2006) and de Gennaro and Jadbabaie (2006) consider convex constraints, while Kim and Mesbahi (2006) deal with a class of nonconvex constraints....
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References
11,658 citations
"On maximizing the second smallest e..." refers background in this paper
...In fact, in several recent works [7], [17], [19], it has been observed that 2(LG) is a measure of stability and robustness of the networked dynamic system....
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...The second smallest eigenvalue of the graph Laplacian LG, also known as the algebraic connectivity of G [4], [8], [14], has emerged as an important parameter in many systems problems defined over networks [7], [12], [15], [17], [20]....
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8,307 citations
"On maximizing the second smallest e..." refers background in this paper
...3The second smallest eigenvalue of L for a graph of order n is bounded from above by n 1 [9]....
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4,377 citations
"On maximizing the second smallest e..." refers background in this paper
...In fact, in several recent works [7], [17], [19], it has been observed that 2(LG) is a measure of stability and robustness of the networked dynamic system....
[...]
...The second smallest eigenvalue of the graph Laplacian LG, also known as the algebraic connectivity of G [4], [8], [14], has emerged as an important parameter in many systems problems defined over networks [7], [12], [15], [17], [20]....
[...]