Abstract
AbstractThis article presents a survey of the current status of the research on structural and qualitative systems theory that has been conducted in the last few decades. This theory can be traced back to the work of Samuelson on comparative static analysis of a national economy. His problem was to find the direction of change in economic equilibrium induced by small changes in the exogenous variables of a system based solely on qualitative information such as the sign pattern of the parameters that specify the system. In the field of engineering, the work of Iri et al. on structural analysis of systems of equations and Lin's research on the structural controllability of dynamic systems were quite influential. Following these pioneering works, a variety of research has been carried out by mathematicians and engineers, as well as by economists. A few examples of problems are the structural solvability and decomposability of systems of equations, the structural characterization of Tinbergen's rule of economic policy, the structural controllability and decouplability of dynamic systems, and the sign‐solvability of static systems. Using graph‐theoretic terms with explanatory examples, this paper surveys the established results on the structural and qualitative analysis of systems in areas ranging from control theory to economics.
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