Analysis of Stability, D-Stability, and Pseudospectra in Economic Modeling
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5657Keywords:
Dynamic stability, $D$-stability, structured singular values, pseudo-spectrum.Abstract
The analysis of dynamic stability is a fundamental and an important concept in system
dynamics. Its focus is on the ability of a dynamical system to return to an equilibrium state
under 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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Copyright (c) 2025 Mutti-Ur Rehman, Sakeena E. M. Hamed, Nidal E. Taha, Arafa O. Mustafa, Khurshidbek Dilmurodov, Hala S. Mahgoub, Mona Magzoub, Runda A. A. Bashir, Mustafa M. Mohammed, Awad A. Bakery
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