New results on \(H_{\infty }\) filtering for fuzzy systems with interval time-varying delays. (English) Zbl 1232.93059
Summary: This paper investigates the problem of \(H_{\infty }\) filtering for continuous Takagi-Sugeno (T-S) fuzzy systems with an interval time-varying delay in the state. Based on the delay partitioning idea, a new approach is proposed for solving this problem, which can achieve much less conservative feasibility conditions. The attention is focused on the design of an \(H_{\infty }\) filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the \(H_{\infty }\) attenuation level from disturbance to estimation error is below a prescribed scalar. The constructed Lyapunov-Krasovskii functional, by applying the delay partitioning method, can potentially guarantee the obtained delay-dependent conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Finally, an example is illustrated to show the reduction in conservatism of the proposed filter design method.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93D20 | Asymptotic stability in control theory |
Keywords:
delay partitioning; fuzzy systems; \(H_{\infty }\) filtering; time-varying delay; asymptotic stabilityReferences:
| [1] | Assawinchaichote, W.; Nguang, S. K., \(H_∞\) filtering for fuzzy dynamic systems with \(D\) stability constraints, IEEE Trans. Circuits Syst. (I), 50, 11, 1503-1508 (2003) · Zbl 1368.93155 |
| [2] | Assawinchaichote, W.; Nguang, S. K.; Shi, P., Robust \(H_∞\) fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps, Inform. Sci., 177, 1699-1714 (2007) · Zbl 1113.93078 |
| [3] | de Souza, C. E.; Fragoso, M. D., \(H_∞\) filtering for Markovian jump linear systems, Int. J. Syst. Sci., 33, 11, 909-915 (2002) · Zbl 1045.93045 |
| [4] | de Souza, C. E.; Li, X., Delay-dependent robust \(H_∞\) control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321 (1999) · Zbl 1041.93515 |
| [5] | Du, B.; Lam, J.; Shu, Z.; Wang, Z., A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components, IET Control Theory Appl., 3, 4, 383-390 (2009) |
| [6] | Feng, G., Robust \(H_∞\) filtering of fuzzy dynamic systems, IEEE Trans. Aerosp. Electron. Syst., 41, 2, 658-671 (2005) |
| [7] | Feng, G., A survey on analysis and design of model-based fuzzy control systems, IEEE Trans. Fuzzy Syst., 14, 5, 676-697 (2006) |
| [8] | Fridman, E.; Shaked, U.; Xie, L., Robust \(H_∞\) filtering of linear systems with time-varying delay, IEEE Trans. Automat. Control, 48, 1, 159-165 (2003) · Zbl 1364.93797 |
| [9] | Gao, H.; Wang, C., A delay-dependent approach to robust \(H_∞\) filtering for uncertain discrete-time state-delayed systems, IEEE Trans. Signal Process., 52, 6, 1631-1640 (2004) · Zbl 1369.93175 |
| [10] | Gao, H.; Wang, Z.; Wang, C., Improved \(H_∞\) control of discrete-time fuzzy systems: a cone complementarity linearization approach, Inform. Sci., 175, 1-2, 57-77 (2005) · Zbl 1113.93308 |
| [11] | Gouaisbaut, F.; Peaucelle, D., Delay-dependent stability analysis of linear time delay systems, IFAC TDC’06 (2006) |
| [12] | Gu, K., A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems, Int. J. Robust Nonlinear Control, 3, 1-14 (1999) · Zbl 0923.93046 |
| [13] | He, Y.; Wang, Q. G.; Xie, L. H.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Trans. Automat. Control, 52, 2, 293-299 (2007) · Zbl 1366.34097 |
| [14] | Hyun, C.-H.; Park, C.-W.; Kim, S., Takagei-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design, Inform. Sci., 180, 11, 2314-2327 (2010) · Zbl 1214.93063 |
| [15] | Iwasaki, T.; Hara, S., Well-posedness of feedback systems: Insight into exact robustness analysis and approximate computations, IEEE Trans. Automat. Control, 43, 5, 619-630 (1998) · Zbl 0927.93038 |
| [16] | Jiang, X.; Han, Q.-L., Robust \(H_∞\) control for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay, IEEE Trans. Fuzzy Syst., 15, 2, 321-331 (2007) |
| [17] | Lam, J.; Gao, H.; Wang, C., Stability analysis for continuous systems with two additive time-varying delay components, Syst. Control Lett., 56, 1, 16-24 (2007) · Zbl 1120.93362 |
| [18] | Lin, C.; Wang, Q. G.; Lee, T. H., Stabilization of uncertain fuzzy time-delay systems via variable structure control approach, IEEE Trans. Fuzzy Syst., 13, 6, 787-798 (2005) |
| [19] | Lin, C.; Wang, Q. G.; Lee, T. H., Stability and stabilization of a class of fuzzy time-delay descriptor systems, IEEE Trans. Fuzzy Syst., 14, 4, 542-551 (2006) |
| [20] | Lin, C.; Wang, Q. G.; Lee, T. H.; Chen, B., \(H_∞\) filter design for nonlinear systems with time-delay through T-S fuzzy model approach, IEEE Trans. Fuzzy Syst., 16, 3, 739-746 (2008) |
| [21] | Ling, Q.; Lemmon, M. D., Stability of quantized control systems under dynamic bit assignment, IEEE Trans. Automat. Control, 50, 5, 734-740 (2005) · Zbl 1365.93470 |
| [22] | Liu, H.; Sun, F.; He, K.; Sun, Z., Design of reduced-order \(H_∞\) filter for Markovian jumping systems with time delay, IEEE Trans. Circuits Syst. (II), 51, 607-612 (2004) |
| [23] | Liu, H.; Sun, F.; Hu, Y. N., \(H_∞\) control for fuzzy singularly perturbed systems, Fuzzy Sets Syst., 155, 272-291 (2005) · Zbl 1140.93356 |
| [24] | Liu, H.; Sun, F.; Sun, Z. Q., Stability analysis and synthesis of fuzzy singularly perturbed systems, IEEE Trans. Fuzzy Syst., 13, 2, 273-284 (2005) |
| [25] | Peaucelle, D.; Arzelier, D.; Henrion, D.; Gouaisbaut, F., Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation, Automatica, 43, 795-804 (2007) · Zbl 1119.93356 |
| [26] | Qiu, J. B.; Feng, G.; Yang, J., Improved delay-dependent \(H_∞\) filtering design for discrete-time polytopic linear delay systems, IEEE Trans. Circuits Syst. (II), 55, 2, 178-182 (2008) |
| [27] | Qiu, J. B.; Feng, G.; Yang, J., New results on robust \(H_∞\) filtering design for discrete piecewise linear delay systems, Int. J. Control, 82, 1, 183-194 (2009) · Zbl 1154.93348 |
| [28] | Safonov, M. G., Stability and robustness of multivariable feedback systems, (Signal Processing, Optimization, and Control (1980), MIT Press) · Zbl 0552.93002 |
| [29] | Shi, P., Filtering on sampled-data systems with parametric uncertainty, IEEE Trans. Automat. Control, 43, 7, 1022-1027 (1998) · Zbl 0951.93050 |
| [30] | Shi, P.; Boukas, E. K.; Agarwal, R. K., Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE Trans. Automat. Control, 44, 8, 1592-1597 (1999) · Zbl 0986.93066 |
| [31] | Tanaka, K.; Wang, H. O., Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (2001), Wiley: Wiley New York |
| [32] | Wang, X. Z.; Dong, C. R., Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy, IEEE Trans. Fuzzy Syst., 17, 3, 556-567 (2009) |
| [33] | Wang, X. Z.; Zhai, J. H.; Lu, S. X., Induction of multiple fuzzy decision trees based on rough set technique, IEEE Trans. Fuzzy Syst., 178, 16, 3188-3202 (2008) · Zbl 1154.68529 |
| [34] | Wang, Z.; Ho, D. W.C.; Liu, Y.; Liu, X., Robust \(H_∞\) control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica, 45, 3, 684-691 (2009) · Zbl 1166.93319 |
| [35] | Wang, Z.; Yang, F.; Ho, D.; Liu, X., Robust \(H_∞\) filtering for stochastic time-delay systems with missing measurements, IEEE Trans. Signal Process., 54, 7, 2579-2587 (2006) · Zbl 1373.94729 |
| [36] | Wu, H.; Li, H. X., New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy control systems with time-varying delay, IEEE Trans. Fuzzy Syst., 15, 3, 482-493 (2007) |
| [37] | Wu, L.; Zheng, W., \(L_2\)−\(L_∞\) fuzzy control of nonlinear stochastic delay systems via dynamic output feedback, IEEE Trans. Syst., Man Cybern. - Part B, 39, 5, 1308-1315 (2009) |
| [38] | Xie, L.; Soh, Y. C., Robust Kalman filtering for uncertain systems, Syst. Control Lett., 22, 123-129 (1994) · Zbl 0792.93118 |
| [39] | Xu, S.; Chen, T., Reduced-order \(H_∞\) filtering for stochastic systems, IEEE Trans. Signal Process., 50, 12, 2998-3007 (2002) · Zbl 1369.94325 |
| [40] | Xu, S.; Lam, J., Exponential \(H_∞\) filter design for uncertain Takagi-Sugeno fuzzy systems with time delay, Eng. Appl. Artif. Intell., 17, 645-659 (2004) |
| [41] | Xu, S.; Lam, J., A survey of linear matrix inequality techniques in stability analysis of delay systems, Int. J. Syst. Sci., 39, 12, 1095-1113 (2008) · Zbl 1156.93382 |
| [42] | Xu, S.; Lam, J.; Zou, Y., \(H_∞\) filtering for singular systems, IEEE Trans. Automat. Control, 48, 12, 2217-2222 (2003) · Zbl 1364.93229 |
| [43] | Yang, J.; Zhong, S.; Li, G.; Luo, W., Robust \(H_∞\) filter design for uncertain fuzzy neutral systems, Inform. Sci., 179, 20, 3697-3710 (2009) · Zbl 1171.93351 |
| [44] | Zhang, B.; Zhou, S.; Li, T., A new approach to robust and non-fragile \(H_∞\) control for uncertain fuzzy systems, Inform. Sci., 177, 22, 5118-5133 (2007) · Zbl 1120.93019 |
| [45] | Zhang, J.; Xia, Y.; Tao, R., New results on \(H_∞\) filtering for fuzzy time-delay systems, IEEE Trans. Fuzzy Syst., 17, 1, 128-137 (2009) |
| [46] | Zhao, Y.; Gao, H.; Lam, J.; Du, B., Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach, IEEE Trans. Fuzzy Syst., 17, 4, 750-762 (2009) |
| [47] | Zhou, S.; Lam, J.; Xue, A. K., \(H_∞\) filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach, Fuzzy Sets Syst., 158, 180-193 (2007) · Zbl 1110.93034 |
| [48] | Zhou, S.; Li, T., Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function, Fuzzy Sets Syst., 151, 1, 139-153 (2005) · Zbl 1142.93379 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
