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A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory

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  • Chacha Stephen Chacha

Abstract

Matrix equations are of foundational importance in the modeling, investigation, and control of dynamical systems. This review discusses various classes of matrix equations, their solutions, and their relevance in control theory and dynamical systems. Key topics include Lyapunov and Riccati equations, iterative techniques such as Krylov subspace approaches and the alternating direction implicit technique, and the influence of condition numbers on numerical robustness. In addition, model-order reduction methods and reduced-order models are examined for their impact on transient behavior and computational efficiency. Finally, emerging directions such as data-driven methodologies, the Koopman operator perspective, and quantum computing are explored, alongside outstanding challenges and prospects for future research.

Suggested Citation

  • Chacha Stephen Chacha, 2025. "A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory," Journal of Applied Mathematics, Hindawi, vol. 2025, pages 1-23, October.
    • Handle: RePEc:hin:jnljam:3745816
    DOI: 10.1155/jama/3745816
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