Complete Stability Analysis for Delayed Economic Systems

Jun-Xiu Chen, Gao-Xia Fan () and Xu Li
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Jun-Xiu Chen: Department of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, China
Gao-Xia Fan: State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
Xu Li: School of Modern Posts, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Mathematics, 2025, vol. 13, issue 13, 1-17

Abstract: In this paper, we will study the stability of economic systems with delay, also called delayed economic systems. We focus on the complete stability problem with respect to delay for linearized economic systems. First, we will review three types of delayed economic systems and will see that the characteristic functions are all in the form f ( λ , τ ) . Then, we will solve the complete stability problem by using the frequency-sweeping approach, which is introduced for the stability studies of economic systems (for the first time). As a consequence, the complete stability problem with delayed economic systems can be systematically solved. Finally, numerical examples will show that the whole stability set of τ for a delayed economic system may be determined accurately.

Keywords: complete stability analysis; frequency-sweeping approach; economic systems; stability; time delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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