Abstract
In this paper, stability conditions based on graph theory for dynamical network systems are shown. Although many frameworks based on graph theory for analysis of dynamical systems have been proposed, there is no stability condition that can be utilized to design of controllers and observers for linear dynamical systems. In this work, to show the stability condition based on graph theory for control and estimation, the dynamical system is represented by a directed graph with weights. The proposed stability conditions are obtained as the inequality of the weighted degrees defined in this paper. As applications, equilibrium point analysis of Lotka-Volterra system and design of pinning controllers and observers for consensus systems are proposed.
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