Abstract
In this article, we deal with the consensus problem of multiple partial-state coupled linear systems, which are neutrally stable. These systems communicate over dynamic undirected networks, which change continuously and can be disconnected at any time. We develop an analysis framework from uniform complete observability theory to work out <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the necessary and sufficient conditions</i> for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">if and only if</i> a jointly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\delta,T)$</tex-math></inline-formula> -connected condition and an observability condition relying only on system and input matrices are satisfied. A lower bound of the convergence rate is also provided. We figure out the proof by applying matrix analysis and linear functional analysis. A simulation example is presented to illustrate our theoretical findings.
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