Fixed-Structure Robust Feedback Linearization for Full Relative Degree Nonlinear Systems

Vlad Mihaly; Mircea Șușcă; Petru Dobra

doi:10.1109/JAS.2025.125354

Volume 12 Issue 10

Oct. 2025

IEEE/CAA Journal of Automatica Sinica

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V. Mihaly, M. Șușcă, and P. Dobra, “Fixed-structure robust feedback linearization for full relative degree nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2026–2039, Oct. 2025. doi: 10.1109/JAS.2025.125354

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V. Mihaly, M. Șușcă, and P. Dobra, “Fixed-structure robust feedback linearization for full relative degree nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2026–2039, Oct. 2025. doi: 10.1109/JAS.2025.125354

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Fixed-Structure Robust Feedback Linearization for Full Relative Degree Nonlinear Systems

doi: 10.1109/JAS.2025.125354

Funds: The work was funded by the project new smart and adaptive robotics solutions for personalized minimally invasive surgery in cancer treatment − ATHENA, European Union – NextGenerationEU and Romanian Government, under National Recovery and Resilience Plan for Romania (CF116/15.11.2022), through the Romanian Ministry of Research, Innovation and Digitalization (within Component 9, investment I8)

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Author Bio:
Vlad Mihaly (Member, IEEE) received the B.S. and M.S. degrees in systems engineering as valedictorian from the Technical University of Cluj-Napoca (TUC-N), Romania in 2018 and 2020, respectively, the Ph.D. degree in systems engineering from TUC-N with summa cum laude, Romania in 2024. Between 2018 and 2020, he was an Associate Teaching Staff Member at the Department of Automation, while between 2021 and 2025 he became a Teaching Assistant and Research Assistant. Since 2025 he is a Lecturer and Researcher at the same department. His research interests include system theory, robust control, nonlinear control, Lyapunov methods, optimizations, and advanced control techniques for medical robots implied in minimally invasive surgeries. He is an IEEE CSS Member since 2018 and IFAC/SRAIT Member since 2019. His Ph.D. thesis deals with fixed structure robust synthesis for nonlinear systems. The main goal of his thesis is to develop a set of techniques to design fixed-structure controllers for classes of nonlinear systems that manage to deal with uncertainties in a similar manner to the μ-synthesis principle

Mircea Șușcă (Member, IEEE) received the B.S. and M.S. degrees in systems engineering as valedictorian from the Technical University of Cluj-Napoca (TUC-N), Romania in 2017 and 2019, respectively, the Ph.D. degree in systems engineering with summa cum laude, from TUC-N, Romania in 2023. During 2017−2019, he was an Associate Teaching Staff Member at the Department of Automation, while between 2020−2024, he became a Teaching and Research Assistant. Since 2025, he is a Lecturer and Researcher at the same department. His main research interests include robust control of linear and nonlinear systems, controller redesign techniques to minimize performance degradation from continuous-time to discrete-time domains, and consensus with additional performance enforcing in multi-agent distributed network systems. He is an IEEE Control Systems Society Member since 2017, an IFAC/SRAIT Member since 2019, and a SIAM Member since 2020

Petru Dobra (Member, IEEE) received the B.S. and M.S. degrees in systems engineering from the Technical University of Cluj-Napoca (TUC-N), Romania in 1984, and the PhD degree in system engineering from TUC-N, Romania in 1998. He is a Full Professor at the Department of Automation, the Technical University of Cluj-Napoca (TUC-N), Romania since 2002, and an Engineer in the field of Automation & Control. Additionally, he is the Doctoral School Director of TUC-N, Romania since 2017. His research interest include systems theory, modeling and identification of industrial processes in the domains of electronics, electricity, mechanics and building automation.He is an IEEE CSS Member since 2015, and is also Active in the Romanian Society of Automation and Technical Informatics (SRAIT) representing the International Federation of Automatic Control (IFAC) in Romania, being the President of the Cluj-Napoca local branch. Through his teaching and research activity, he involved students in the development of bachelor’s, master’s and doctoral theses in both theoretical and applied studies, especially in the fields of low-power electric actuators, embedded control and dynamic thermal modeling. He is the Author of many scientific works published in various highly-ranked journals and conferences organized under the IEEE Control System Society and the IFAC. He contributed as an Organizer and Editor to the IFAC Workshop on Convergence of Information Technologies and Control Methods with Power Plants and Power Systems in the years 2007 and 2013
Corresponding author: Vlad Mihaly, e-mail: vlad.mihaly@aut.utcluj.ro
Received Date: 2024-08-30
Accepted Date: 2025-02-21

Abstract

Abstract

The exact feedback linearization method implies an accurate knowledge of the model and its parameters. This assumption is an inherent limitation of the method, suffering from robustness issues. In general, the model structure is only partially known and its parameters present uncertainties. The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriately-designed robust control layer. This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction. We consider the case of full relative degree input-affine nonlinear systems, which are of great practical importance in the literature. The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties. The constructive proofs provide exact representations of the uncertainty models in three considered scenarios: unmatched, fully-matched, and partially-matched uncertainties. The uncertainty model will be a descriptor system, which also represents one of the novelties of the paper. Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives. The end-to-end procedure is emphasized on an illustrative example, in two different hypotheses.
- Feedback linearization,
- nonlinear control,
- robustness,
- uncertain nonlinear systems

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References

[1]	R. W. Brockett, “Feedback invariants for nonlinear systems,” IFAC Proceedings Volumes, vol. 11, no. 1, pp. 1115–1120, Jun. 1978. doi: 10.1016/S1474-6670(17)66062-2
[2]	A. Isidori, Nonlinear Control Systems, 3rd Ed. London, UK: Springer, 1995.
[3]	H. K. Khalil, Nonlinear Control, Global Edition, 1st Ed. Edinburgh Gate, UK: Pearson Education Limited, 2015.
[4]	K. Majd, M. Razeghi-Jahromi, and A. Homaifar, “A stable analytical solution method for car-like robot trajectory tracking and optimization,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 39–47, Jan. 2020. doi: 10.1109/JAS.2019.1911816
[5]	A. Isidori, “The zero dynamics of a nonlinear system: From the origin to the latest progresses of a long successful story,” European J. Control, vol. 19, no. 5, pp. 369–378, Sept. 2013. doi: 10.1016/j.ejcon.2013.05.014
[6]	A. P. Aguiar, J. P. Hespanha, and P. V. Kokotovic, “Performance limitations in reference tracking and path following for nonlinear systems,” Automatica, vol. 44, pp. 598–610, Mar. 2008. doi: 10.1016/j.automatica.2007.06.030
[7]	S. Jiffri, P. Paoletti, and J. E. Mottershead, “Feedback linearization in systems with nonsmooth nonlinearities,” J. Guidance, Control, and Dynamic, vol. 39, no. 4, pp. 1–12, Feb. 2016. doi: 10.2514/1.G001220
[8]	W. Respondek, “Orbital feedback linearization of single-input nonlinear control systems,” IFAC Proc. Volumes, vol. 31, no. 17, pp. 483–488, Jul. 1998. doi: 10.1016/S1474-6670(17)40383-1
[9]	S. J. Li and W. Respondek, “Orbital feedback linearization for multi-input control systems,” Int. J. Robust and Nonlinear Control, vol. 25, no. 9, pp. 1352–1378, Jun. 2015.
[10]	D. A. Fetisov, “A-Orbital feedback linearization of multiinput control affine systems,” Int. J. Robust and Nonlinear Control, vol. 30, pp. 5602–5627, Jul. 2020. doi: 10.1002/rnc.5099
[11]	D. A. Fetisov, “On some approaches to linearization of affine systems,” Proc. 11th IFAC Sympo. Nonlinear Control Systems, Vienna, Austria, 2019, pp. 700–705.
[12]	J. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, “State-space solutions to standard $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ control problems,” IEEE Trans. Autom Control, vol. 34, pp. 831–847, Aug. 1989. doi: 10.1109/9.29425
[13]	P. Gahinet, and P. Apkarian, “A linear matrix inequality approach to $\mathcal{H}_{\infty}$ control,” Int. J. Robust and Nonlinear Control, vol. 4, pp. 421–448, Apr. 1994. doi: 10.1002/rnc.4590040403
[14]	P. Apkarian, “The $\mathcal{H}_{\infty}$ control problem is solved,” in Design and Validation of Aerospace Control Systems, Aerospace Lab, Issue 13, Onera, France, 2017, pp. 1–11.
[15]	A. Packard, J. Doyle, and G. Balas, “Linear multivariable robust control with a μ perspective,” J. Dyn. Syst. Measure. and Control, vol. 115, pp. 426–438, Jun. 1993. doi: 10.1115/1.2899083
[16]	P. Apkarian, “Nonsmooth μ synthesis,” Int. J. Robust and Nonlinear Control, vol. 21, pp. 1493–1508, Spet. 2011. doi: 10.1002/rnc.1644
[17]	S. Skogestad and I. Postlethwaite, Multivariable Feedback Control - Analysis and Design, New York, USA: John Wiley & Sons, 2005.
[18]	L. B. Freidovich and H. K. Khalil, “Performance recovery of feedback-linearization-based designs,” IEEE Trans. Autom. Control, vol. 53, no. 10, pp. 2324–2334, Nov. 2008. doi: 10.1109/TAC.2008.2006821
[19]	H. R. Karimi and M. R. J. Motlagh, “Robust feedback linearization control for a non linearizable MIMO Nonlinear system in the presence of model uncertainties,” in Proc. IEEE Int. Conf. Service Operations and Logistics, and Informatics, Shanghai, China, 2006, pp. 965–970.
[20]	M. Kaheni, M. H. Zarif, A. A. Kalat, and L. Chisci, “Robust feedback linearization for input-constrained nonlinear systems with matched uncertainties,” in Proc. European Control Conf., Limassol, Cyprus, 2018, pp. 2947–2952.
[21]	M. Kaheni, M. H. Zarif, A. A. Kalat, and L. Chisci, “Radial pole path approach for fast response of affine constrained nonlinear systems with matched uncertainties,” Int. J. Robust and Nonlinear Control, vol. 30, pp. 142–158, Oct. 2019. doi: 10.1002/rnc.4757
[22]	N. Wang and B. Kiss, “A Method to Robustify Exact Linearization Against Parameter Uncertainty,” Int. J. Control, Autom. and Systems, vol. 17, pp. 1–11, Jan. 2019. doi: 10.1007/s12555-017-0703-0
[23]	W. Yin, L. Sun, M. Wang, and J. Liu, “Position control of a series elastic actuator based on global sliding mode controller design,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 850–858, Mar. 2019. doi: 10.1109/JAS.2019.1911498
[24]	Y. Wu, A. Isidori, R. Lu, and H. K. Khalil, “Performance recovery of dynamic feedback-linearization methods for multivariable nonlinear systems,” IEEE Trans. Autom. Control, vol. 65, no. 4, pp. 1365–1380, Apr. 2020. doi: 10.1109/TAC.2019.2924176
[25]	T. Westenbroek, D. Fridovich-Keil, E. Mazumdar, S. Arora, V. Prabhu, S. S. Sastry, and C. J. Tomlin, “Feedback linearization for uncertain systems via reinforcement learning,” in Proc. IEEE Int. Conf. Robotics and Automation, Paris, France, 2020, pp. 1364–1371.
[26]	R. G. Goswami, P. Krishnamurthy, and F. Khorrami, “Data-driven deep learning based feedback linearization of systems with unknown dynamics,” in Proc. American Control Conf, San Diego, USA, 2023, pp. 66–71.
[27]	A. Nicoletti and A. Karimi, “Robust controller design for linear systems with nonlinear distortions. A Data-Driven Approach,” in Proc. European Control Conf., Limassol, Cyprus, 2018, pp. 1–6.
[28]	H. Oersted and Y. Ma, Geometric and Feedback Linearization on UAV: Review, arXiv preprint arXiv 2311.06774, 2023.
[29]	M. Hajaya and T. Shaqarin, “Control of a benchmark CSTR using feedback linearization,” Jordanian J. Engineering and Chemical Industries, vol. 2, no. 3, pp. 67–75, Mar. 2019.
[30]	Z. Shulong, A. Honglei, Z. Daibing, and S. Lincheng, “A new feedback linearization LQR control for attitude of quadrotor,” in Proc. 13th Int. Conf. Control, Automation, Robotics & Vision, Singapore, 2014, pp. 1593–1597.
[31]	C. Lascu, I. Boldea, and F. Blaabjerg, “Direct torque control via feedback linearization for permanent magnet synchronous motor drives,” in Proc. 13th Int. Conf. Optimization of Electrical and Electronic Equipment, 2012, pp. 338–343.
[32]	M. Rokonuzzaman, N. Mohajer, S. Nahavandi, and S. Mohamed, “Review and performance evaluation of path tracking controllers of autonomous vehicles,” IET Intelligent Transport Syst., vol. 15, pp. 646–670, Mar. 2021. doi: 10.1049/itr2.12051
[33]	K. Poolla, P. Khargonekar, A. Tikku, J. Krause, and K. Nagpal, “A time-domain approach to model validation,” IEEE Trans. Autom. Control, vol. 39, no. 5, pp. 951–959, May 1994. doi: 10.1109/9.284871
[34]	G. Balas, R. Chiang, A. Packard, and M. Safonov, Robust Control Toolbox^TM Reference, Version 6.11.2 (R2022b), Sept. 2022. [Online], Available: https://www.mathworks.com/help/pdf_doc/robust/robust_ug.pdf.
[35]	M. Șușcă, V. Mihaly, and P. Dobra, “Nonconvex valid uncertainty modelling approach for robust control synthesis,” in Proc. 27th Int. Conf. System Theory, Control and Computing, Timișoara, Romania, 2023, pp.269–276.
[36]	M. Șușcă, V. Mihaly, M. Stănese, and P. Dobra, “Uncertainty modelling of mechanical systems with derivative behaviour for robust control synthesis,” in Proc. European Control Conf., Bucharest, Romania, 2023, pp. 1–7.

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Fixed-Structure Robust Feedback Linearization for Full Relative Degree Nonlinear Systems

doi: 10.1109/JAS.2025.125354

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