This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.
[1] H. K. Khalil, "Feedback control of nonstandard singularly perturbed
systems," IEEE Trans. Automat. Contr., vol. 34, pp. 1052-1060,
1989.
[2] Z. Gajic and M. Lim, "A new filtering method for linear singularly
perturbed systems," IEEE Trans. Automat. Contr., vol. 39, pp. 1952-
1955, 1994.
[3] X. Shen and L. Deng, "Decomposition solution of H∞ filter gain in
singularly perturbed systems," Signal Processing, vol. 55, pp. 313-
320, 1996.
[4] M.T. Lim and Z. Gajic, "Reduced-Order H∞ optimal filtering for
systems with slow and fast modes," IEEE Trans. Circuits and Systems
I, vol. 47, pp. 250-254, 2000.
[5] P. Shi and V. Dragan, "Asymptotic H∞ control of singularly perturbed
system with parametric uncertainties," IEEE Trans. Automat.
Contr., vol. 44, pp. 1738-1742, 1999.
[6] P. V. Kokotovic, H. K. Khalil, and J. O-Reilly, Singular Perturbation
Methods in Control: Analysis and Design, London: Academic Press,
1986
[7] 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.
[8] K. Tanaka, T. Taniguchi, and H. O. Wang, "Fuzzy control based
on quadratic performance function - A linear matrix inequality
approach," in Proc. IEEE Conf. Decision and Contr., pp. 2914-2919,
1998.
[9] B. S. Chen, C. S. Tseng, and H. J. Uang, "Mixed H2/H∞ fuzzy
output feedback control design for nonlinear dynamic systems: An
LMI approach," IEEE Trans. Fuzzy Syst., vol. 8, pp. 249-265, 2000.
[10] L. Xie, M. Fu, and C. E. de Souza, "H∞ control and quadratic stabilisation
of systems with parameter uncertainty via output feedback,"
IEEE Trans. Automat. Contr., vol. 37, pp. 1253-1256, 1992.
[11] S. K. Nguang, "Robust nonlinear H∞ output feedback control,"
IEEE Trans Automat. Contr., vol. 41, pp. 1003-1008, 1996.
[12] S. K. Nguang and M. Fu, "Robust nonlinear H∞ filtering," Automatica,
vol. 32, pp. 1195-1199, 1996.
[13] K. Tanaka, T. Ikeda, and H. O. Wang, "Robust stabilization of a
class of uncertain nonlinear systems via fuzzy control: Quadratic
stabilizability, H∞ control theory, and linear matrix inequality",
IEEE Trans. Fuzzy Syst., vol. 4, pp. 1-13, 1996.
[14] M. Teixeira and S. H. Zak, "Stabilizing controller design for uncertain
nonlinear systems using fuzzy models", IEEE Trans. Fuzzy Syst.,
vol. 7, pp. 133-142, 1999.
[15] S. H. Zak, "Stabilizing fuzzy system models using linear controllers",
IEEE Trans. Fuzzy Syst., vol. 7, pp. 236-240, 1999.
[16] L. X. Wang, A course in fuzzy systems and control. Englewood Cliffs,
NJ: Prentice-Hall, 1997.
[17] S. K. Nguang and P. Shi, "H∞ fuzzy output feedback control design
for nonlinear systems: An LMI approach ," IEEE Trans. Fuzzy Syst.,
vol. 11, pp. 331-340, 2003.
[18] 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.
[19] W.Assawinchaichote and S. K. Nguang, "H∞ filtering for nonlinear
singularly perturbed systems with pole placement constraints: An
LMI approach", IEEE Trans. Signal Processing, vol. 52, pp. 579-
588, 2004.
[1] H. K. Khalil, "Feedback control of nonstandard singularly perturbed
systems," IEEE Trans. Automat. Contr., vol. 34, pp. 1052-1060,
1989.
[2] Z. Gajic and M. Lim, "A new filtering method for linear singularly
perturbed systems," IEEE Trans. Automat. Contr., vol. 39, pp. 1952-
1955, 1994.
[3] X. Shen and L. Deng, "Decomposition solution of H∞ filter gain in
singularly perturbed systems," Signal Processing, vol. 55, pp. 313-
320, 1996.
[4] M.T. Lim and Z. Gajic, "Reduced-Order H∞ optimal filtering for
systems with slow and fast modes," IEEE Trans. Circuits and Systems
I, vol. 47, pp. 250-254, 2000.
[5] P. Shi and V. Dragan, "Asymptotic H∞ control of singularly perturbed
system with parametric uncertainties," IEEE Trans. Automat.
Contr., vol. 44, pp. 1738-1742, 1999.
[6] P. V. Kokotovic, H. K. Khalil, and J. O-Reilly, Singular Perturbation
Methods in Control: Analysis and Design, London: Academic Press,
1986
[7] 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.
[8] K. Tanaka, T. Taniguchi, and H. O. Wang, "Fuzzy control based
on quadratic performance function - A linear matrix inequality
approach," in Proc. IEEE Conf. Decision and Contr., pp. 2914-2919,
1998.
[9] B. S. Chen, C. S. Tseng, and H. J. Uang, "Mixed H2/H∞ fuzzy
output feedback control design for nonlinear dynamic systems: An
LMI approach," IEEE Trans. Fuzzy Syst., vol. 8, pp. 249-265, 2000.
[10] L. Xie, M. Fu, and C. E. de Souza, "H∞ control and quadratic stabilisation
of systems with parameter uncertainty via output feedback,"
IEEE Trans. Automat. Contr., vol. 37, pp. 1253-1256, 1992.
[11] S. K. Nguang, "Robust nonlinear H∞ output feedback control,"
IEEE Trans Automat. Contr., vol. 41, pp. 1003-1008, 1996.
[12] S. K. Nguang and M. Fu, "Robust nonlinear H∞ filtering," Automatica,
vol. 32, pp. 1195-1199, 1996.
[13] K. Tanaka, T. Ikeda, and H. O. Wang, "Robust stabilization of a
class of uncertain nonlinear systems via fuzzy control: Quadratic
stabilizability, H∞ control theory, and linear matrix inequality",
IEEE Trans. Fuzzy Syst., vol. 4, pp. 1-13, 1996.
[14] M. Teixeira and S. H. Zak, "Stabilizing controller design for uncertain
nonlinear systems using fuzzy models", IEEE Trans. Fuzzy Syst.,
vol. 7, pp. 133-142, 1999.
[15] S. H. Zak, "Stabilizing fuzzy system models using linear controllers",
IEEE Trans. Fuzzy Syst., vol. 7, pp. 236-240, 1999.
[16] L. X. Wang, A course in fuzzy systems and control. Englewood Cliffs,
NJ: Prentice-Hall, 1997.
[17] S. K. Nguang and P. Shi, "H∞ fuzzy output feedback control design
for nonlinear systems: An LMI approach ," IEEE Trans. Fuzzy Syst.,
vol. 11, pp. 331-340, 2003.
[18] 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.
[19] W.Assawinchaichote and S. K. Nguang, "H∞ filtering for nonlinear
singularly perturbed systems with pole placement constraints: An
LMI approach", IEEE Trans. Signal Processing, vol. 52, pp. 579-
588, 2004.
@article{"International Journal of Electrical, Electronic and Communication Sciences:61445", author = "Wudhichai Assawinchaichote and Sing Kiong Nguang", title = "Robust H∞ Filter Design for Uncertain Fuzzy Descriptor Systems: LMI-Based Design", abstract = "This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.
", keywords = "H∞ control, Takagi-Sugeno (TS) fuzzy model, Linear Matrix Inequalities (LMIs), Descriptor systems.", volume = "1", number = "9", pages = "1365-6", }
