Continuous and discrete stability criteria comparison

Authors

  • Baltazar Aguirre Hernández Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco #186, Col. Leyes de Reforma, 1ra. Sección, Iztapalapa 09340, México. https://orcid.org/0000-0002-6227-5232
  • Edgar Cristian Díaz González Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, CDMX, Mexico
  • Carlos Arturo Loredo Villalobos Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana - Azcapotzalco, CDMX, Mexico https://orcid.org/0000-0003-1641-1704
  • Tatiana Sánchez Alcántara Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, CDMX, Mexico

Keywords:

Hurwitz polynomials, Schur polynomials, Kharitonov´s Theorem

Abstract

A wide range of phenomena that evolve over time can be modeled and analyzed using both continuous and discrete-time systems. Choosing the appropriate type of system depends on the nature of the problem being studied and its constraints. For any engineer or scientist working on the design of dynamical systems, a thorough understanding of both types of systems is essential. In this paper explain some differences between the stability criteria in continuous linear systems and discrete linear systems.

References

F. R. Gantmacher. The theory of matrices. Vol. 131. American Mathematical Soc., 2000.

D. Hinrichsen and A.J. Pritchard. Mathematical Systems Theory I: Modelling, State Space Analysis, Stability andRobustness. Texts in Applied Mathematics. Springer Berlin Heidelberg, 2011.

B. Aguirre-Hernández et al. “Estabilidad de sistemas por medio de polinomios Hurwitz”. In: Revista deMatemática: Teoría y Aplicaciones 24.1 (2017), pp. 61–77. doi: 10.15517/rmta.v24i1.27751.

Z. Zahreddine. “Explicit relationships between Routh-Hurwitz and Schur-Cohn types of stability”. In: IrishMath. Soc. Bull. 29 (1992), pp. 49–54.

B. R. Barmish and C. L. DeMarco. “Criteria for Robust Stability of Systems with Structured Uncertainty: APerspective”. In: 1987 American Control Conference. 1987, pp. 476–481. doi: 10.23919/ACC.1987.4789367.

Z. Zahreddine. “Symmetric properties of Routh–Hurwitz and Schur–Cohn stability criteria”. In: Symmetry 14.3(2022), p. 603.

J.E. Marsden and M.J. Hoffman. Basic Complex Analysis. W. H. Freeman, 1999.

S.P. Bhattacharyya, H. Chapellat, and L.H. Keel. Robust Control: The Parametric Approach. Prentice-Hall informa-tion and system sciences series. Prentice Hall PTR, 1995.

S.P. Bhattacharyya, A. Datta, and L.H. Keel. Linear control theory: structure, robustness, and optimization. CRCpress, 2018.

H. Parastvand et al. “Robust placement and sizing of charging stations from a novel graph theoretic perspective”. In: IEEE Access 8 (2020), pp. 118593–118602.

G. Oaxaca-Adams, R. Villafuerte-Segura, and B. Aguirre-Hernández. “On Hurwitz stability for families ofpolynomials”. In: International Journal of Robust and Nonlinear Control 34.7 (2024), pp. 4576–4594.

G. Oaxaca-Adams, R. Villafuerte-Segura, and B. Aguirre-Hernández. “On Schur stability for families ofpolynomials”. In: Journal of the Franklin Institute 361.4 (2024), p. 106644.19

Additional Files

Published

2025-12-17

How to Cite

Aguirre Hernández, B., Díaz González, E. C., Loredo Villalobos, C. A., & Sánchez Alcántara, T. (2025). Continuous and discrete stability criteria comparison. Journal of Dynamical Systems and Complexity , 1(1), 12–19. Retrieved from https://revista.amesdyc.org/index.php/JDSC/article/view/2

Issue

Vol. 1 No. 1 (2025): Special welcome number

Section

Applied Mathematics and Interdisciplinary Applications

License

Copyright (c) 2025 Baltazar Aguirre Hernández, Edgar Cristian Díaz González, Carlos Arturo Loredo Villalobos, Tatiana Sánchez Alcántara

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.