A Survey on H∞ Control-Based Output Feedback Techniques

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Volume: 13 | Issue: 5 | Pages: 11517-11523 | October 2023 | https://doi.org/10.48084/etasr.6056

Abstract

The study of 2-D discrete systems has always been a preferred choice amongst researchers and academics, due to its diversified applications in most practical applications. For more than two decades, research based on H control techniques has been the focus of attention, as it plays a key role in the design and development of various applications based on signal processing and control theory. In many practical applications, the accessibility of the state vectors is not possible, and, in such cases, output feedback techniques are most appropriate. This paper presents a detailed survey based on H control-based output feedback techniques for discrete 2-D systems.

 

 

Keywords:

2-D discrete system, robust stability, asymptotic stability control, static output feedback controller, dynamic output feedback controller, observer based output feedback controller, bounded real lemma

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References

R. Roesser, "A discrete state-space model for linear image processing," IEEE Transactions on Automatic Control, vol. 20, no. 1, pp. 1–10, Feb. 1975.

E. Fornasini and G. Marchesini, "State-space realization theory of two-dimensional filters," IEEE Transactions on Automatic Control, vol. 21, no. 4, pp. 484–492, Aug. 1976.

E. Fornasini and G. Marchesini, "Doubly-indexed dynamical systems: State-space models and structural properties," Mathematical systems theory, vol. 12, no. 1, pp. 59–72, Dec. 1978.

J. Kurek, "The general state-space model for a two-dimensional linear digital system," IEEE Transactions on Automatic Control, vol. 30, no. 6, pp. 600–602, Jun. 1985.

N. Zerroug, K. Behih, Z. Bouchama, and K. Zehar, "Robust Adaptive Fuzzy Control of Nonlinear Systems," Engineering, Technology & Applied Science Research, vol. 12, no. 2, pp. 8328–8334, Apr. 2022.

O. P. Bharti, R. K. Saket, and S. K. Nagar, "Controller Design For DFIG Driven By Variable Speed Wind Turbine Using Static Output Feedback Technique," Engineering, Technology & Applied Science Research, vol. 6, no. 4, pp. 1056–1061, Aug. 2016.

D. Bakria, M. Azzouzi, and D. Gozim, "Chaos Control and Stabilization of a PID Controlled Buck Converter Using the Spotted Hyena Optimizer," Engineering, Technology & Applied Science Research, vol. 11, no. 6, pp. 7922–7926, Dec. 2021.

G. Zames, "Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses," IEEE Transactions on Automatic Control, vol. 26, no. 2, pp. 301–320, Apr. 1981.

J. Doyle, K. Glover, P. Khargonekar, and B. Francis, "State-space solutions to standard H2 and H∞ control problems," in 1988 American Control Conference, Atlanta, GA, USA, Jun. 1988, pp. 1691–1696.

B. Hassibi, A. H. Sayed, and T. Kailath, Indefinite-Quadratic Estimation and Control: A Unified Approach to H2 and H-infinity Theories. Philadelphia, PA, USA: SIAM, 1999.

B. A. Francis, A course in H control theory. Berlin, Germany: Springer-Verlag, 1987.

Z. Y. Feng, L. Xu, and Y. Anazawa, "Sufficient LMI conditions for H∞ static output feedback control of 2-D systems," in 2010 11th International Conference on Control Automation Robotics & Vision, Singapore, Sep. 2010, pp. 57–60.

C. K. Ahn, P. Shi, and M. V. Basin, "Two-Dimensional Dissipative Control and Filtering for Roesser Model," IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1745–1759, Jul. 2015.

Z. Duan and Z. Xiang, "Output Feedback H∞ Stabilization of 2-D Discrete Switched Systems in FM LSS Model," Circuits, Systems, and Signal Processing, vol. 33, no. 4, pp. 1095–1117, Apr. 2014.

H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, "Robust Hınfty Fuzzy Output-Feedback Control With Multiple Probabilistic Delays and Multiple Missing Measurements," IEEE Transactions on Fuzzy Systems, vol. 18, no. 4, pp. 712–725, Dec. 2010.

Y. Zhao and Y. Qu, "The 36th Chinese Control Conference [Conference Reports]," IEEE Control Systems Magazine, vol. 38, no. 2, pp. 109–113, Apr. 2018.

C. Du, L. Xie, and C. Zhang, "H∞ control and robust stabilization of two-dimensional systems in Roesser models," Automatica, vol. 37, no. 2, pp. 205–211, Feb. 2001.

Z. Duan and Z. Xiang, "H2 output feedback controller design for discrete-time 2-D switched systems," Transactions of the Institute of Measurement and Control, vol. 36, no. 1, pp. 68–77, Feb. 2014.

Z.-Y. Feng and L. Xu, "H∞ static output feedback controller design for two-dimensional discrete systems in Roesser model," in 2010 IEEE International Symposium on Computer-Aided Control System Design, Yokohama, Japan, Sep. 2010, pp. 1790–1794.

Z. Y. Feng, L. Xu, M. Wu, and J.-H. She, "H∞ Static Output Feedback Control of 2-D Discrete Systems in FM Second Model," Asian Journal of Control, vol. 14, no. 6, pp. 1505–1513, 2012.

L. Li, "Observer-based H∞ controller for 2-D T–S fuzzy model," International Journal of Systems Science, vol. 47, no. 14, pp. 3455–3464, Oct. 2016.

L. Li, X. Li, and S. Ye, "Dynamic output feedback H∞ control for 2-D fuzzy systems," ISA Transactions, vol. 95, pp. 1–10, Dec. 2019.

Y. Luo, Z. Wang, J. Liang, G. Wei, and F. E. Alsaadi, "H_ınfty Control for 2-D Fuzzy Systems With Interval Time-Varying Delays and Missing Measurements," IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 365–377, Oct. 2017.

V. C. Pal and R. Negi, "Robust output feedback control of 2-D discrete systems with actuator saturation and time-varying delay," Transactions of the Institute of Measurement and Control, vol. 39, no. 11, pp. 1673–1695, Nov. 2017.

D. Peng and X. Guan, "Output Feedback H∞ Control for 2-D State-Delayed Systems," Circuits, Systems & Signal Processing, vol. 28, no. 1, pp. 147–167, Feb. 2009.

L. Xie, C. Du, Y. C. Soh, and C. Zhang, "H∞ and Robust Control of 2-D Systems in FM Second Model," Multidimensional Systems and Signal Processing, vol. 13, no. 3, pp. 265–287, Jul. 2002.

H. Xu, Y. Zou, S. Xu, and L. Guo, "Robust H∞ Control for Uncertain Two-Dimensional Discrete Systems Described by the General Model via Output Feedback Controllers," International Journal of Control, Automation, and Systems, vol. 6, no. 5, pp. 785–791, Oct. 2008.

R. Yang, L. Xie, and C. Zhang, "H2 and mixed H2/H∞ control of two-dimensional systems in Roesser model," Automatica, vol. 42, no. 9, pp. 1507–1514, Sep. 2006.

K. Zhou, J. C. Doyle, and K. Glover, Robust and optimal control. Upper Saddle River, NJ, USA: Prentice Hall, 1996.

K. Glover and J. C. Doyle, "A state space approach to H∞ optimal control," in Three Decades of Mathematical System Theory: A Collection of Surveys at the Occasion of the 50th Birthday of Jan C. Willems, H. Nijmeijer and J. M. Schumacher, Eds. Berlin, Germany: Springer, 1989, pp. 179–218.

B. Francis, J. Helton, and G. Zames, "H∞-optimal feedback controllers for linear multivariable systems," IEEE Transactions on Automatic Control, vol. 29, no. 10, pp. 888–900, Oct. 1984.

C. Du, L. Xie, and Y. C. Soh, "H∞ filtering of 2-D discrete systems," IEEE Transactions on Signal Processing, vol. 48, no. 6, pp. 1760–1768, Jun. 2000.

C. Scherer, P. Gahinet, and M. Chilali, "Multiobjective output-feedback control via LMI optimization," IEEE Transactions on Automatic Control, vol. 42, no. 7, pp. 896–911, Jul. 1997.

P. Apkarian, P. Gahinet, and G. Becker, "Self-scheduled H∞ control of linear parameter-varying systems: a design example," Automatica, vol. 31, no. 9, pp. 1251–1261, Sep. 1995.

E. I. L. Ghaoui, F. Oustry, and M. Ait Rami, "A cone complementarity linearization algorithms for static output feedback and related problems," IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1171–1176, 1997.

H. Xu, Y. Zou, S. Xu, and J. Lam, "Bounded real lemma and robust H∞ control of 2-D singular Roesser models," Systems & Control Letters, vol. 54, no. 4, pp. 339–346, Apr. 2005.

S. Kririm and A. Hmamed, "Robust H∞ filtering for uncertain 2-D singular systems with delays," in 2019 8th International Conference on Systems and Control (ICSC), Marrakesh, Morocco, Jul. 2019, pp. 88–93.

K. H. Lee, J. H. Lee, and W. H. Kwon, "Sufficient LMI conditions for H∞ output feedback stabilization of linear discrete-time systems," IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 675–680, Apr. 2006.

H. Gao, Z. Wang, and C. Wang, "Improved H∞ control of discrete-time fuzzy systems: a cone complementarity linearization approach," Information Sciences, vol. 175, no. 1, pp. 57–77, Sep. 2005.

P. Gahinet, A. Nemirovskii, A. J. Laub, and M. Chilali, "The LMI control toolbox," in Proceedings of 1994 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA, Sep. 1994, vol. 3, pp. 2038–2041 vol.3.

S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA, USA: SIAM, 1994.

Z. Y. Feng, J. She, and L. Xu, "A brief review and insights into matrix inequalities for H∞ static-output-feedback control and a local optimal solution," International Journal of Systems Science, vol. 50, no. 12, pp. 2292–2305, Sep. 2019.

Y. W. Wang, X.-K. Liu, J. W. Xiao, and Y. Shen, "Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control," Automatica, vol. 93, pp. 26–32, Jul. 2018.

J. K. Goyal, S. Ghosh, and S. Kamal, "New LMI conditions for H∞/H2 output feedback control of linear discrete-time systems," International Journal of Control, vol. 94, no. 6, pp. 1716–1722, Jun. 2021.

J. Chen, C. Lin, B. Chen, and Q. G. Wang, "Improved stability criterion and output feedback control for discrete time-delay systems," Applied Mathematical Modelling, vol. 52, pp. 82–93, Dec. 2017.

X.-H. Chang, R.-R. Liu, and J. H. Park, "A Further Study on Output Feedback mathcalH_ınfty Control for Discrete-Time Systems," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 2, pp. 305–309, Oct. 2020.

E. Pathan, A. A. Bakar, S. A. Zulkifi, M. H. Khan, H. Arshad, and M. Asad, "A Robust Frequency Controller based on Linear Matrix Inequality for a Parallel Islanded Microgrid," Engineering, Technology & Applied Science Research, vol. 10, no. 5, pp. 6264–6269, Oct. 2020.

O. Aydogdu and M. L. Levent, "Kalman State Estimation and LQR Assisted Adaptive Control Of a Variable Loaded Servo System," Engineering, Technology & Applied Science Research, vol. 9, no. 3, pp. 4125–4130, Jun. 2019.

C. Lin, B. Chen, and Q.-G. Wang, "Static output feedback stabilization for fractional-order systems in T-S fuzzy models," Neurocomputing, vol. 218, pp. 354–358, Dec. 2016.

R. Yang, S. Ding, and W. X. Zheng, "Co-design of event-triggered mechanism and dissipativity-based output feedback controller for two-dimensional systems," Automatica, vol. 130, Aug. 2021, Art. no. 109694.

X. Lv, Y. Niu, and Z. Cao, "Sliding Mode Control for Uncertain 2-D FMII Systems Under Stochastic Scheduling," IEEE Transactions on Cybernetics, pp. 1–12, 2023.

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How to Cite

[1]
G. P. Pandiya and A. Vidyarthi, “A Survey on H∞ Control-Based Output Feedback Techniques”, Eng. Technol. Appl. Sci. Res., vol. 13, no. 5, pp. 11517–11523, Oct. 2023.

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