Robust H State-Feedback Control Design for Nonlinear Time-Varying Delay Systems Based on An LMI Approach

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Published: Jan 3, 2008
DOI: https://doi.org/10.37936/ecti-eec.200862.171775
Keywords:
H control, Time-varying delay Fuzzy systems Linear Matrix Inequality (LMI)

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Wudhichai Assawinchaichote
Department of Electronic and Telecommnunication Engineering, King Mongkut's University of Technology Thonburi

Abstract

This paper examines the problem of designing a robust Hgif.latex?\infty state-feedback controller for a class of nonlinear systems with time-varying delay described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a robust Hgif.latex?\infty state-feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.

Article Details

How to Cite
Assawinchaichote, W. (2008). Robust H State-Feedback Control Design for Nonlinear Time-Varying Delay Systems Based on An LMI Approach. ECTI Transactions on Electrical Engineering, Electronics, and Communications, 6(2), 126–133. https://doi.org/10.37936/ecti-eec.200862.171775
Issue
Vol. 6 No. 2 (2008): Regular Issue
Section
Research Article

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References

[1] M. S. Mahmoud and N. F. Al-Muthairi, "Design of robust controllers for time delay systems," IEEE Trans. Automat. Contr., vol. 39, pp. 995-999, 1994.

[2] H. H. Choi and M. J. Chung, "Memoryless H controller design for linear systems with delayed state and control," Automatica, vol. 31, pp. 917-919, 1995.

[3] E. T. Jeung, J. H. Kim, and H. B. Park, "H output feedback controller design for linear systems with time-varying delayed state," IEEE Trans. Automat. Contr., vol. 43, pp. 971-974, 1998.

[4] J. A. Ball and J. W. Helton, "H control for nonlinear plants: Connection with differential games," IEEE Conf. Decision and Contr., pp. 956-962, 1989.

[5] A. Isidori and A. Asto¯, "Disturbance attenuation and H-control via measurement feedback in nonlinear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 1283-1293, 1992.

[6] D. J. Hill and P. J. Moylan, "Dissipative dynamical systems: basic input-output and state properties," J. Franklin Inst., vol. 309, pp. 327-357, 1980.

[7] J. C. Willems, "Dissipative dynamic systems Part I: General theory," Arch. Raitonal Mech. Anal., vol. 45, pp. 321-351, 1972.

[8] A. J. van der Schaft, "A state-space approach to nonlinear H control," Syst. Contr. Letters, vol. 16, pp. 1-8, 1991.

[9] Z. X. Han and G. Feng, "State-feedback H controller design of fuzzy dynamic system using LMI techniques," Fuzzy-IEEE'98, pp. 538-544, 1998.

[10] K. Tanaka, T. Ikeda, and H. O. Wang, "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stability, H control theory, and linear martix inequality," IEEE Trans. Fuzzy. Syst., vol. 4, pp. 1-13, 1996.

[11] H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues," IEEE Trans. Fuzzy Syst., vol. 4, pp. 14-23, 1996.

[12] Y. Y. Cao and P. M. Frank, "Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models," Fuzzy Sets Syst., vol. 124, pp. 213-229, 2001.

[13] K. R. Lee, J. H Kim, E. T Jeung, and H. B. Park, "Output feedback robust H control of uncertain fuzzy dynamic systems with time-varying delay," IEEE Trans. Fuzzy. Syst., vol. 8, pp. 657-664, 2000.

[14] R. J. Wang, W. W. Lin, and W. J. Wang, "Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems," IEEE Trans. Syst., Man, Cybern. Part B, vol. 34, pp. 1-4, 2004.

[15] S. K. Nguang and P. Shi, "Stabilisation of a class of nonlinear time-delay systems using fuzzy models," Proc. IEEE Conf. Decision and Contr., pp. 4415-4419, 2000.

[16] S. K. Nguang and W. Assawinchaichote, "H filtering for fuzzy dynamic systems with pole placement," IEEE Trans. Circuits Systs. I, vol. 50, pp. 1503-1508, 2003.

[17] W. Assawinchaichote and S. K. Nguang, "H filtering for fuzzy singularly perturbed systems with pole placement constraints: An LMI approach" IEEE Trans. Signal Processing, vol. 52, pp. 579-588, 2004.

[18] W. Assawinchaichote and S. K. Nguang, "Robust H state-feedback control design for fuzzy singularly perturbed system with Markovian jumps: An LMI approach" Trans. Electrical Eng. Electronics and Communications, vol. 3, pp. 175-184, 2005.

[19] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, vol. 15, Philadelphia: SIAM, 1994.