Abstract
During the analysis and design of a network system, a frequently encountered situation is when the network structure is <i>known</i> but the node dynamics is practically <i>unknown</i>. Thus, structural analysis in which the prior knowledge is mostly about the network structure has received attention in recent years. Motivated by this line of research, this article focuses on a structural design problem called the <i>structural equilibrium control problem</i>, which is used to find a sign pattern in the control input such that any constant input with the sign pattern drives the system to a desirable steady state in a qualitative sense. A solution is presented by reducing it to a design problem of the so-called <i>sign-solvable equation</i>, which is a linear equation whose qualitative solution can be determined from the prior knowledge of the sign pattern of the coefficients.
Highlights
During the analysis and design of a network system, one is frequently faced with a situation where the prior information about a system is quite limited
Structural analysis, which is to determine a qualitative property of a network system from the prior knowledge of the network structure, has been conducted
We assume that the full information of the network structure and the qualitative information of the node dynamics are available
Summary
During the analysis and design of a network system, one is frequently faced with a situation where the prior information about a system is quite limited. A typical case is when the network structure is known but the node dynamics is unknown except for the qualitative properties. This study presents the solution to the structural equilibrium control problem for a class of network systems. In these systems, the node dynamics and network structure are given as a set of monotonically coupled differential equations and an edge-labeled directed graph, respectively. Consider an edge-labeled directed graph G = (V, E, L) for the node set V ⊆ {1, 2, . (A4) allows us to represent the network structure of Σ as an edge-labeled directed graph G = (V, E, L) for the node set V := {1, 2, .
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