Vol. 2 Núm. 1 (2019): Edición especial


Visión Actual

Laplace transform and its applications into dynamic systems: a review

Transformada de Laplace y sus aplicaciones en sistemas dinámicos: una revisión


Palabras clave:

Señales, Transformada de Laplace, Ecuaciones diferenciales, Sistemas Dinámicos, Sistemas de Control, Reactor multipropósito (es).

Palabras clave:

Signals, Laplace Transform, Differential Equations, Dynamic Systems, Control Systems, Multipurpose reactor (en).

Resumen (en)

This paper presents a review of Laplace Transform (LT) applications in the analysis of linear dynamic systems. Is presented the importance of the transforms; the definition of the Transform; theorems and properties with applications and finally, the use of LT for the calculation of: steady state error, transfer functions, ordinary differential equations solution, frequency responses, signal analysis and block diagrams. The modeling and operational analysis with LT of a multipurpose reactor is proposed as a didactic situation for academic purposes.

Resumen (es)

Este artículo presenta una revisión sobre las aplicaciones de la transformada de Laplace (TL) en el análisis de sistemas dinámicos lineales. Se presenta la importancia de la transformada; la definición de la transformada; los teoremas y propiedades con aplicaciones y por último, aplicaciones del uso de la TL para el cálculo de: error de estado estacionario, funciones de transferencia, solución de ecuaciones diferenciales ordinarias, respuestas en frecuencia, análisis de señales y diagramas de bloques. Se propone, como situación didáctica para propósitos académicos, el modelamiento y análisis operacional con TL de un reactor multipropósito.


M. F. Golnaraghi, B. C. Kuo, and M. F. Golnaraghi, Automatic control systems. Hoboken, NJ: Wiley, 2010.

R. T. Stefani and B. Shahian, Design of feedback control systems. New York; Oxford: Oxford University Press, 2001.

T. E. Fortmann and K. L. Hitz, An introduction to linear control systems. New York, NY: Marcel Dekker, 2000.

K. Ogata, Ingeniería de control moderna. Madrid: Pearson Educación, 2003.

N. Lobontiu, “The Laplace Transform,” in System Dynamics for Engineering Students, Elsevier, 2018, pp. 273–322.

N. S. Nise, Control systems engineering. Hoboken, NJ: Wiley, 2015.

J. J. DiStefano, A. R. Stubberud, and I. J. Williams, Schaum’s outline of theory and problems of feedback and control systems. New York: McGraw-Hill, 1995 [Online]. Available:

M. R. Spiegel, Schaum’s outline of theory and problems of Laplace transforms. New York: McGraw-Hill, 2006.

E. Maya, “Métodos y técnicas de investigación,” 2014 [Online]. Available:

R. hernandez Samperini, C. fernandez Callado, and P. baptista Lucio, Metodología de la investigación, 6 ta. MC GRAW HILL, 2014.

L. C. Calderón, O. L. Londoño, and L. F. Maldonado, Guía para construir estados del arte. 2014.

M. J. Corinthios, “Complex-variable distribution theory for Laplace and z transforms,” IEE Proc. - Vision, Image, Signal Process., vol. 152, no. 1, p. 97, Dec. 2005.

H. Chen and Y. Zhang, “Laplace Transform for Stable Random Variables,” in 2015 3rd International Conference on Computer and Computing Science (COMCOMS), 2015, pp. 32–36

M. L. Abell and J. P. Braselton, “Laplace Transform Methods,” in Differential Equations with Mathematica, Elsevier, 2016, pp. 613–720.

X.-S. Yang, “Laplace Transforms,” in Engineering Mathematics with Examples and Applications, Elsevier, 2017, pp. 187–198.

J. Semmlow, “Linear Systems in the Complex Frequency Domain,” in Circuits, Signals and Systems for Bioengineers, Elsevier, 2018, pp. 295–344.

I. S. Gradshteyn and I. M. Ryzhik, “Fourier, Laplace, and Mellin Transforms,” in Table of Integrals, Series, and Products, Elsevier, 2014, pp. 1077–1103.

M. A. Haidekker, “Solving Differential Equations in the Laplace Domain,” in Linear Feedback Controls, Elsevier, 2013, pp. 27–56.

R. F. Hoskins, “The Laplace Transform,” in Delta Functions, Elsevier, 2011, pp. 99–127

W. van Drongelen, “Laplace and z -Transform,” in Signal Processing for Neuroscientists, Elsevier, 2018, pp. 231–250. [Accessed: 20-Aug-2018]

J. Kirkwood, “The Laplace Transform,” in Mathematical Physics with Partial Differential Equations, Elsevier, 2018, pp. 401–425

J. Bird, “Laplace Transforms,” in Engineering Mathematics Pocket Book, Elsevier, 2008, pp. 472–491.

J. Y. Rodriguez and A. E. Diaz, “Transformada de Laplace Inversa.” No publicado, p. 81, 2017.

W. R. Briceño and A. E. Diaz, “Transformada de Laplace directa.” No publicado, Bogotá D.C, p. 212, 2017.

E. A. D. Poularikas, A. D. Poularikas, and S. Seely, Poularikas, A. D., Seely, S . “ Laplace Transforms .” 2000.

D. G. Zill and M. R. Cullen, Ecuaciones diferenciales, Matemáticas avanzadas para ingeniería, vol. 1. 2008.

J. Salvador and C. Peña, “Transformada de Laplace y sus aplicaciones a las ecuaciones diferenciales Índice General,” 2008.

Ingenieria Técnica Industrial, “Tema 4. La Transformada de Laplace,” Ampliación Matemáticas. Espec. Electrónica Ind., no. 1, p. 12, 2009.

J. Chen, K. H. Lundberg, D. E. Davison, and D. S. Bernstein, “The Final Value Theorem Revisited - Infinite Limits and Irrational Functions,” IEEE Control Syst., vol. 27, no. 3, pp. 97–99, Jun. 2007.

X. Espinoza, Manual de fracciones parciales. Cuenca: Editorial Universidad Abya-Yala, 2012.

Z. Cervenanska, J. Kotianova, and A. Strasiftak, “Laplace transform in application using computational knowledge engine,” in 2012 15th International Conference on Interactive Collaborative Learning (ICL), 2012, pp. 1–4.

J. L. Duarte Madrid, E. A. González Querubín, and P. A. Ospina Henao, “MPC in Space State for the Control of a Furuta Pendulum,” A. P. P. Abdul Majeed, J. A. Mat-Jizat, M. H. A. Hassan, Z. Taha, H. L. Choi, and J. Kim, Eds. Singapore: Springer Singapore, 2020, pp. 219–235.

Shuping Dang, Yubo Sun, L. Baker, and A. Gholamzadeh, “Dynamical oil-immersed transformer thermal control model based on thermal-electrical analogy and its analytical solution using laplace transform,” in 2014 14th International Conference on Environment and Electrical Engineering, 2014, pp. 241–244.

M. De La Sen, “On the External Positivity of Linear Time-Invariant Dynamic Systems,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 55, no. 2, pp. 188–192, Feb. 2008

T. At and T. H. E. Origin, “Initial conditions, generalized functions, and the laplace transform troubles at the origin,” IEEE Control Syst., vol. 27, no. 1, pp. 22–35, Feb. 2007

N. Yalcin, E. Celik, and A. Gokdogan, “Multiplicative Laplace transform and its applications,” Optik (Stuttg)., vol. 127, no. 20, pp. 9984–9995, Oct. 2016.

A. G. Bolton, “Design of sampled control systems using laplace domain techniques,” IEE Proc. G (Electronic Circuits Syst., vol. 128, no. 3, p. 138, 1981.

Y. Yan, F. C. Lee, P. Mattavelli, and S. Tian, “Small-signal Laplace-domain model for digital predictive current mode controls,” in 2012 IEEE Energy Conversion Congress and Exposition (ECCE), 2012, pp. 1386–1393.

Q. HONG, Y. SHI, and D. LU, “Dynamics modeling and pressure control of composites tape winding system based on LQSMC,” Chinese J. Aeronaut., May 2019.

Yongji Wang and Hong Wang, “Output PDFs control for linear stochastic systems with arbitrarily bounded random parameters: a new application of the Laplace transform,” Proc. 2002 Am. Control Conf. (IEEE Cat. No.CH37301), vol. 5, pp. 4262–4267 vol.5, 2002.

Q.-C. Zhong, A. Kuperman, and R. K. Stobart, “Filter Design for UDE-based Controllers,” in UKACC International Conference on CONTROL 2010, 2010, vol. 2010, no. 4, pp. 583–588.

H. Yang, F. Wang, and F. Han, “Containment Control of Fractional Order Multi-Agent Systems With Time Delays,” IEEE/CAA J. Autom. Sin., vol. 5, no. 3, pp. 727–732, May 2018.

L. H. I. Lim, Z. Ye, J. Ye, D. Yang, and H. Du, “A linear identification of diode models from single I-V characteristics of PV panels,” IEEE Trans. Ind. Electron., vol. 62, no. 7, pp. 4181–4193, Jul. 2015.

R. Brito, A. Carvalho, and M. Gericota, “A new three-phase voltage sourced converter laplace model,” in 2015 9th International Conference on Compatibility and Power Electronics (CPE), 2015, pp. 160–166.

J. Van de Vegte and J. Li, “Design of Passive Beam Vibration Controls by Multivariable Frequency Domain Control Techniques,” in 1989 American Control Conference, 1989, no. 6, pp. 2796–2801.

J. Li and Y. Hu, “PID controller parameter iterative learning scheme design for missile roll-tunnel model,” in Proceedings of the 30th Chinese Control Conference, CCC 2011, 2011, pp. 2415–2418.

J. Q. Xie and M. Farooq, “Frequency domain stability test of SISO systems with memoryless nonlinear feedback,” in Proceedings of IEEE International Conference on Industrial Technology 2000 (IEEE Cat. No.00TH8482), vol. 1, pp. 206–210.

J. Klima, “Analytical closed-form solution of a space-vector modulated VSI feeding an induction motor drive,” IEEE Trans. Energy Convers., vol. 17, no. 2, pp. 191–196, Jun. 2002.

V. Sooraj and J. L. Febin Daya, “A Large Signal Dynamic Model of Loosely Coupled IPT System for EV Based on Laplace Phasor Transform,” in 2018 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), 2018, vol. 2, pp. 1–6.

Y. N. Rosenvasser, E. Y. Polyakov, and B. P. Lampe, “Application of Laplace transformation for digital redesign of continuous control systems,” IEEE Trans. Automat. Contr., vol. 44, no. 4, pp. 883–886, Apr. 1999.

R. A. O’Connell, “Simple recursive processes for determining Laplace and Z transforms of the zero-input responses of linear time-invariant systems,” IEEE Trans. Educ., vol. 45, no. 2, pp. 168–170, May 2002.

H. R. Miller, D. L. Trumper, and K. H. Lundberg, “A Brief Treatment of Generalized Functions for Use in Teaching the Laplace Transform,” Proc. 45th IEEE Conf. Decis. Control, pp. 3885–3889, 2006.

N. Bayan, S. Erfani, and B. Shahrrava, “Two-dimensional Laplace transform-based analysis for communication systems,” in 48th Midwest Symposium on Circuits and Systems, 2005., 2005, vol. 1, no. 1, pp. 349-350.

N. Nagaoka and T. Ishii, “A logarithmic segmented Laplace transform and its application to a battery diagnosis,” in 2017 52nd International Universities Power Engineering Conference (UPEC), 2017, vol. 2017-Janua, pp. 1–5.

K. Udagawa et al., “Analytic method using laplace transform for a modified TRV of a circuit breaker,” in IEEE PES T&D 2010, 2010, pp. 1–6.

S. Djordjevic, O. H. Bosgra, and P. M. J. Van den Hof, “Boundary control of two-phase fluid flow using the Laplace-space domain,” in Proceedings of the 2011 American Control Conference, 2011, pp. 3283–3288.

J. Liao, N. Zhou, and Q. Wang, “DC-side harmonic analysis and DC filter design in hybrid HVDC transmission systems,” Int. J. Electr. Power Energy Syst., vol. 113, pp. 861–873, Dec. 2019.

W. K. Zahra, M. M. Hikal, and T. A. Bahnasy, “Solutions of fractional order electrical circuits via Laplace transform and nonstandard finite difference method,” J. Egypt. Math. Soc., vol. 25, no. 2, pp. 252–261, Apr. 2017.

A. J. Prado, L. S. Lessa, E. Assuncao, M. C. M. Teixeira, R. C. Monzani, and J. P. Filho, “Laplace’s analyses for application of π circuits’ associations in digital simulations,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 3276–3276.

L. A. Kraft and M. D. Kankam, “Modelling a single phase, voltage controlled rectifier using Laplace transforms,” IEEE Trans. Power Syst., vol. 8, no. 2, pp. 388–394, May 1993.

T. Solyar, “Investigation of the Crack’s Effect on SH-Waves Propagation Based on the Regularized Formula of Inverse Laplace Transform,” in 2018 XXIIIrd International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2018, vol. 1, no. 1, pp. 170–174.

F. Tossani, F. Napolitano, and A. Borghetti, “Inverse Laplace Transform of the Ground Impedance Matrix of Overhead Lines,” IEEE Trans. Electromagn. Compat., vol. 60, no. 6, pp. 2033–2036, Dec. 2018.

R. Nuricumbo-Guillén, F. P. Espino-Cortés, and P. Gómez, “Computation of transient voltage and current profiles along illuminated multiconductor lines by means of the numerical Laplace transform,” IET Gener. Transm. Distrib., vol. 9, no. 13, pp. 1608–1613, Oct. 2015.

S. Erfani and M. Ahmadi, “Fundamentals of generalized Laplace transform techniques for linear time-varying systems,” in ISSCS 2011 - International Symposium on Signals, Circuits and Systems, 2011, no. 3, pp. 1–4.

M. Ahmad and L. Yang, “Laplace transform current density convolution finite-difference time-domain formulation for the modelling of 1D graphene,” IET Microwaves, Antennas Propag., vol. 11, no. 15, pp. 2211–2218, Dec. 2017.

S. Ohnuki, S. Watanabe, and K. Nagasawa, “Time-domain analysis of electromagnetic fields using the fast inverse Laplace transform,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, vol. 146, no. 1, pp. 1786–1786.

S. Kishimoto, S. Ohnuki, Y. Ashizawa, K. Nakagawa, S. Y. Huang, and W. C. Chew, “Time-domain analysis of electromagnetic problems for nanoscale objects by integral equation methods with fast inverse Laplace transform,” in 2013 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), 2013, no. 1, pp. 47–47.

I. G. Enting, “Laplace transform analysis of the carbon cycle,” Environ. Model. Softw., vol. 22, no. 10, pp. 1488–1497, Oct. 2007.

P. Caputo, V. Loise, S. Ashimova, B. Teltayev, R. Vaiana, and C. Oliviero Rossi, “Inverse Laplace Transform (ILT) NMR: A powerful tool to differentiate a real rejuvenator and a softener of aged bitumen,” Colloids Surfaces A Physicochem. Eng. Asp., vol. 574, pp. 154–161, Aug. 2019.

Y. Yang, Z. Cai, and Y. Liu, “Interval analysis of dynamic response of structures using Laplace transform,” Probabilistic Eng. Mech., vol. 29, pp. 32–39, Jul. 2012.

R. E. Williamson, Students solutions manual for use with : Introduction to differential equations and dynamical systems. Boston: McGraw-Hill, 2001.

W. E. Boyce and R. C. DiPrima, Elementary differential equations and boundary value problems. 2012.

R. K. Nagle, E. B. Saff, and A. D. Snider, Fundamentals of differential equations. 2018.

R. Ocampo and E. C. M. Bernal, “Diseño e implementación de un sistema de control pid para la supervisión de la temperatura del reactor multipropósito,” p. 120, 2018 [Online]. Available:

Cómo citar


Briceño Camacho, W. R., Rodríguez-González, J. Y., y Escobar-Díaz, A. (2019). Laplace transform and its applications into dynamic systems: a review. Visión electrónica, 2(1), 199–215.


Briceño Camacho, W.R. et al. 2019. Laplace transform and its applications into dynamic systems: a review. Visión electrónica. 2, 1 (mar. 2019), 199–215. DOI:


Briceño Camacho, W. R.; Rodríguez-González, J. Y.; Escobar-Díaz, A. Laplace transform and its applications into dynamic systems: a review. Vis. Electron. 2019, 2, 199-215.


BRICEÑO CAMACHO, Wilmer Rafael; RODRÍGUEZ-GONZÁLEZ, Jairo Yesid; ESCOBAR-DÍAZ, Andrés. Laplace transform and its applications into dynamic systems: a review. Visión electrónica, [S. l.], v. 2, n. 1, p. 199–215, 2019. DOI: 10.14483/22484728.18425. Disponível em: Acesso em: 27 may. 2024.


Briceño Camacho, Wilmer Rafael, Jairo Yesid Rodríguez-González, y Andrés Escobar-Díaz. 2019. «Laplace transform and its applications into dynamic systems: a review». Visión electrónica 2 (1):199-215.


Briceño Camacho, W. R., Rodríguez-González, J. Y. y Escobar-Díaz, A. (2019) «Laplace transform and its applications into dynamic systems: a review», Visión electrónica, 2(1), pp. 199–215. doi: 10.14483/22484728.18425.


W. R. Briceño Camacho, J. Y. Rodríguez-González, y A. Escobar-Díaz, «Laplace transform and its applications into dynamic systems: a review», Vis. Electron., vol. 2, n.º 1, pp. 199–215, mar. 2019.


Briceño Camacho, Wilmer Rafael, et al. «Laplace transform and its applications into dynamic systems: a review». Visión electrónica, vol. 2, n.º 1, marzo de 2019, pp. 199-15, doi:10.14483/22484728.18425.


Briceño Camacho, Wilmer Rafael, Jairo Yesid Rodríguez-González, y Andrés Escobar-Díaz. «Laplace transform and its applications into dynamic systems: a review». Visión electrónica 2, no. 1 (marzo 13, 2019): 199–215. Accedido mayo 27, 2024.


Briceño Camacho WR, Rodríguez-González JY, Escobar-Díaz A. Laplace transform and its applications into dynamic systems: a review. Vis. Electron. [Internet]. 13 de marzo de 2019 [citado 27 de mayo de 2024];2(1):199-215. Disponible en:

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