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Analysis of Stability, D-Stability, and Pseudospectra in Economic Modeling

Mutti-Ur RehmanCenter of Research and Innovation , Asia International University , Yangiobod MFY , G'ijduvon Street , House 74 , Bukhara , UzbekistanSakeena E. M. HamedUniversity of Jeddah , College of Business at Khulis , Jeddah , Saudi ArabiaNidal E. TahaDepartment of Mathematics , College of Science , Qassim University , Buraidah 51452 , Saudi ArabiaArafa O. MustafaUniversity of Jeddah , College of Business at Khulis , Jeddah , Saudi ArabiaKhurshidbek DilmurodovCenter of Research and Innovation , Asia International University , Yangiobod MFY , G'ijduvon Street , House 74 , Bukhara , UzbekistanHala S. MahgoubUniversity of Jeddah , College of Business at Khulis , Jeddah , Saudi ArabiaMona MagzoubMathematics Department , Applied College at Alkamil , University of Jeddah , Saudi ArabiaRunda A. A. BashirUniversity of Jeddah , Applied College at Khulis , Department of Mathematics , Jeddah , Saudi ArabiaMustafa M. MohammedUniversity of JeddahAwad A. BakeryUniversity of Jeddah , Applied College at Khulis , Department of Mathematics , Jeddah , Saudi Arabia

2025en

ABI

Annotatsiya

The analysis of dynamic stability is a fundamental and an important concept in systemdynamics. Its focus is on the ability of a dynamical system to return to an equilibrium stateunder structured perturbations. The study of dynamic stability plays critical role in various fields,for instance, engineering, control theory, and economics. The analysis on the dynamic stability mostly involves computation of the eigenvalues of a system’s state matrix. The D-stability is a particular and specialized form of dynamic stability, and its mainly focus dynamical systems subject to structured perturbations. In this paper, we present new results on dynamic stability, and D-stability of a class of linear economic model in the mathematical form $$y_t = Ay_t + By_{t-1} + Cx_t,$$ with $y_t$ is a vector of the endogenous variables, xt is a vector of exogenous variables, and A, B, and C are the matrices having an appropriate dimensions. The new results are developed on both necessary and sufficient conditions on the interconnection between D-stable matrices and structured singular values. The numerical experimentation show the behaviour of structured singular values for matrices appearing across linear dynamic model.

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DOI: 10.29020/nybg.ejpam.v18i1.5657

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