非线性时滞奇异系统的鲁棒同时H控制
Nonlinear Singular Systems with Time-Delay Robust Simultaneous H Control

作者: 李瑞杰 , 包俊东 :内蒙古师范大学,数学科学学院,内蒙古 呼和浩特;

关键词: 非线性奇异系统时滞线性矩阵不等式鲁棒同时H&infin控制Nonlinear Singular Systems Time-Delay Linear Matrix Inequality Robust Simultaneous H-Infinity Control

摘要:
针对一组具有不确定性状态非线性的时滞奇异系统鲁棒H控制问题进行研究。基于Lyapunov-Krasovskii泛函和线性矩阵不等式(LMI)以及非线性不确定向量函数范数有界的条件下,得到自由奇异系统的稳定性判据,进而有状态反馈控制下闭环非线性时滞奇异系统的正则、无脉冲、稳定的充分条件。给出带有不确定性具有扰动的非线性时滞闭环系统的H控制器的构造方法。最后,给出仿真算例说明本文方法的可行性。

Abstract: This paper considers the problems of robust simultaneous H-infinity control for nonlinear singular systems with uncertain state time-delay. The stabilization criterion for singular systems is derived by Lyapunov-Krasovskii functional, linear matrix inequality (LMI) and nonlinear uncertain vector function with norm bounded, then the sufficient condition of closed-loop nonlinear singular systems with time-delay is gained to guarantee regular, impulse-free, stable. The H-infinity controller design approach is given for nonlinear uncertain singular closed-loop systems with time-delay and distur-bance. Finally, a numerical example is presented to illustrate the feasibility of the proposed results.

文章引用: 李瑞杰 , 包俊东 (2015) 非线性时滞奇异系统的鲁棒同时H控制。 动力系统与控制, 4, 45-53. doi: 10.12677/DSC.2015.43006

参考文献

[1] Xie, X.S. and Liu, Y.Q. (1996) On stabilization of linear singular systems with time delay. Journal of South China University of Technology (Natural Science), 24, 38-43.

[2] 冯俊娥, 程兆林 (2003) 线性广义时滞系统的 状态反馈控制器. 控制与决策, 3, 159-163.

[3] 张冬雯, 王春红 (2006) 时滞不确定奇异系统的鲁棒 控制. 电机与控制学报, 5, 537-540.

[4] 杨帆, 张庆灵 (2006) 基于神经网络的时滞广义系统的鲁棒 控制. 控制工程, 3, 324-326.

[5] 徐胜元, 杨成梧 (2000) 一类不确定性广义非线性系统的鲁棒控制. 控制理论与应用, 4, 624-625.

[6] 王德进 (2004) 一类非线性不确定非线性时滞系统的时滞依赖鲁棒控制. 控制与决策, 6, 675-679.

[7] 傅勤, 曲文波, 杨成梧 (2007) 带有界扰动的一类非线性系统系统的鲁棒控制. 自动化学报, 11, 1209-1210.

[8] 王岩青, 姜长生 (2005) 一类非线性不确定时滞系统的鲁棒 控制. 信息与控制, 2, 147-151.

[9] 王天成, 高在瑞 (2009) 一类不确定非线性广义时滞系统的 控制. 控制工程, 5, 614-617.

[10] Saeks, R. and Murray, J. (1982) Fractional representation, algebraic geometry, and the simultaneous stabilization problem. IEEE Transactions On Automatic Control, 27, 895-903.
http://dx.doi.org /10.1109/TAC.1982.1103005

[11] 曹永岩, 孙优贤 (1998) 同时镇定问题研究. 信息与控制, 3, 161-166.

[12] Cao, Y.Y., Sun, Y.X. and Lam, J. (1999) Simultaneous stabilization via static output feedback and state feedback. IEEE Transactions On Automatic Control, 44, 1277-1282

[13] 关强, 何冠生, 王龙, 郁文生 (2011) 线性系统的同时镇定问题. 控制理论与应用, 1, 1-10.

[14] Masubuchi, I., Suda, N. and Ohara, A. (1998) LMI-Based controller synthesis: A unified formulation and solution. International Journal of Robust and Nonlinear Control, 8, 669-686.
http://dx.doi.org /10.1002/(SICI)1099-1239(19980715)8:8<669::AID-RNC337>3.0.CO;2-W

[15] Xie, L. and De Souza, C.E. (1990) Robust control for linear time-invariant systems with norm-bounded uncertainty in the input matrix. Systems & Control Letters, 14, 389-396.
http://dx.doi.org /10.1016/0167-6911(90)90088-C

[16] Dai, L. (1989) Singular control systems. Springer-Verlag, Berlin.
http://dx.doi.org /10.1007/BFb0002475

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