New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay.

*(English)*Zbl 1194.93117Summary: This paper is concerned with the stability problem of uncertain T-S fuzzy systems with time-varying delay by employing a further improved free-weighting matrix approach. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov-Krasovskii functional. Finally, two numerical examples are given to demonstrate the effectiveness and the merits of the proposed methods.

##### MSC:

93C42 | Fuzzy control/observation systems |

34H05 | Control problems involving ordinary differential equations |

93D99 | Stability of control systems |

93C05 | Linear systems in control theory |

##### Keywords:

T-S fuzzy systems; time-varying delay; delay-dependent stability; Lyapunov-Krasovskii functional; linear matrix inequalities (LMIs)
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\textit{F. Liu} et al., Fuzzy Sets Syst. 161, No. 15, 2033--2042 (2010; Zbl 1194.93117)

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##### References:

[1] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE transactions systems man cybernetics, 15, 116-132, (1985) · Zbl 0576.93021 |

[2] | Tanaka, K.; Sano, M., A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer, IEEE transactions on fuzzy systems, 2, 119-134, (1994) |

[3] | Chen, B.S.; Tseng, C.S.; Uang, H.J., Mixed \(H_2 / H_\infty\) fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach, IEEE transactions on fuzzy systems, 8, 249-265, (2000) |

[4] | Wang, H.O.; Tanaka, K.; Griffin, M.F., An approach to fuzzy control of nonlinear systems: stability and design issues, IEEE transactions on fuzzy systems, 4, 14-23, (1996) |

[5] | Teixeira, M.C.; Zak, S.H., Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE transactions on fuzzy systems, 7, 133-144, (1999) |

[6] | Ying, H., The takagi – sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers, Automatica, 34, 157-167, (1998) · Zbl 0989.93053 |

[7] | Akar, M.; Ozguner, U., Decentralized techniques for the analysis and control of takagi – sugeno fuzzy systems, IEEE transactions on fuzzy systems, 8, 691-704, (2000) |

[8] | Cao, Y.Y.; Frank, P.M., Stability analysis and synthesis of nonlinear time-delay systems via linear takagi – sugeno fuzzy models, Fuzzy sets and systems, 124, 213-229, (2001) · Zbl 1002.93051 |

[9] | W.J. Chang, W. Chang, Fuzzy control of continuous time-delay affine T-S fuzzy systems, in: Proc. 2004 IEEE Internat. Conf. on Networking, Sensing and Control Taipei, Taiwan, 2004, pp. 618-623. |

[10] | Ding, B.C.; Sun, H.X.; Yang, P., Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in takagi – sugeno’s form, Automatica, 42, 503-508, (2006) · Zbl 1123.93061 |

[11] | Tian, E.G.; Peng, C., Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay, Fuzzy sets and systems, 157, 544-559, (2006) · Zbl 1082.93031 |

[12] | Guan, X.P.; Chen, C.L., Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, IEEE transactions on fuzzy systems, 12, 236-249, (2004) · Zbl 1142.93363 |

[13] | Yoneyama, J., Robust control analysis and synthesis for uncertain fuzzy systems with time-delay, IEEE international conference on fuzzy systems, 1, 396-401, (2003) |

[14] | Wu, H.N.; Li, H.X., New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay, IEEE transactions on fuzzy systems, 15, 482-493, (2007) |

[15] | Lin, C.; Wang, Q.G.; Lee, T.H.; He, Y.; Chen, B., Observer-based \(H_\infty\) fuzzy control design for T-S fuzzy systems with state delays, Automatica, 44, 868-874, (2008) · Zbl 1283.93164 |

[16] | Liu, X.D.; Zhang, Q.L., New approaches to \(H_\infty\) controller designs based on fuzzy observers for T-S fuzzy systems via LMI, Automatica, 39, 1571-1582, (2003) · Zbl 1029.93042 |

[17] | Luo, Y.B.; Cao, Y.Y.; Sun, Y.X., Robust stability of uncertain takagi – sugeno fuzzy systems with time-varying input-delay, Acta automatica sinica, 34, 87-92, (2008) |

[18] | Chen, B.; Liu, X.P.; Tong, S.C.; Lin, C., Observer-based stabilization of T-S fuzzy systems with input delay, IEEE transactions on fuzzy systems, 16, 652-663, (2008) |

[19] | Lin, C.; Wang, Q.G.; Lee, T.H.; Chen, B., \(H_\infty\) filter design for nonlinear systems with time-delay through T-S fuzzy model approach, IEEE transactions on fuzzy systems, 16, 739-746, (2008) |

[20] | Moon, Y.S.; Park, P.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, International journal of control, 74, 1447-1455, (2001) · Zbl 1023.93055 |

[21] | Li, C.G.; Wang, H.J.; Liao, X.F., Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays, IEE proceedingsâ€”control theory and applications, 151, 417-421, (2004) |

[22] | He, Y.; Wu, M.; She, J.H.; Liu, G.P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems & control letters, 51, 57-65, (2004) · Zbl 1157.93467 |

[23] | Chen, B.; Liu, X.P.; Tong, S.C., New delay-dependent stabilization conditions of T-S systems with constant delay, Fuzzy sets and systems, 158, 2209-2224, (2007) · Zbl 1122.93048 |

[24] | Lien, C.H., Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay, Chaos, solitons and fractals, 28, 422-427, (2006) · Zbl 1091.93022 |

[25] | Lien, C.H.; Yu, K.W.; Chen, W.D.; Wan, Z.L.; Chung, Y.J., Stability criteria for uncertain takagi – sugeno fuzzy systems with interval time-varying delay, IET control theory and applications, 1, 746-769, (2007) |

[26] | Boyd, S.; Ghaoui, L.E.; Feron, E., Linear matrix inequality in system and control theory, () |

[27] | Petersen, I.R.; Hollot, C.V., A Riccati equation approach to the stabilization of uncertain linear systems, Automatica, 22, 397-411, (1986) · Zbl 0602.93055 |

[28] | Peng, C.; Tian, Y.C.; Tian, E.G., Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay, Fuzzy sets and systems, 159, 2713-2729, (2008) · Zbl 1170.93344 |

[29] | Peng, C.; Tian, Y.C., Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay, Journal of computational and applied mathematics, 214, 480-494, (2008) · Zbl 1136.93437 |

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