Citation: | YANG Ying, HUANG Lin. Absolute Stabilization Related to Circle Criterion: an LMI-Based Approach[J]. Applied Mathematics and Mechanics, 2003, 24(8): 805-811. |
[1] |
Lur'e A I,Postnikov V N.On the theory of stability of control systems[J].Prikl Mat Meh,1944,8(3).
|
[2] |
Popov V.Absolute stability of non-linear systems of automatic control[J].Automation and Remote Control,1961,22:857-875.
|
[3] |
Narendra K S,Taylor J H.Frequency Domain Criteria for Absolute Stability[M].New York:Academic Press,1973.
|
[4] |
Vidyasagar M.Nonlinear System Analysis[M].Englewood Cliffs,NJ:Prentice Hall,1993.
|
[5] |
Khalil H K.Nonlinear System[M].New York:MacMillan Pubishing,1992.
|
[6] |
Boyd S,Chaoui L E,Feron E,et al.Linear Matrix Inequalities in System and Control Theory[M].Philadelphia,Pennsylvania:SIAM,1994.
|
[7] |
Savkin A V,Petersen I R.A connection between H∞ control and the absolute stabilizability of uncertain systems[J].System and Control Letters,1994,23(3):197-203.
|
[8] |
Konishi K,Kokame H.Robust stability of Lur'e systems with time-varying uncertainties:a linear matrix inequality approach[J].Int J Systmes Science,1999,30(1):3-9.
|
[9] |
Kahutani Y,Hagiwara T,Araki M.LMI representation of the shifted of Popov criterion[J].Automatica,2000,36(5):765-770.
|
[10] |
Gahinet P,Arkadi Nemirovski,Laub J A,et al.LMI Control Toolbox User's Guide[M].Natick,Mass:The Math Works,Inc,1995.
|
[11] |
Iwasaki,Skelton R E.All controllers for the general H∞ control problem:LMI existence conditions and state space formulas[J].Automatica,1994,30(8):1307-1317.
|
[12] |
Izumi Masubuchi,Atsumi Ohara,Nobuhide Suda.LMI-based controller synthesis:a unified formulation and solution[J].Int J Robust Nonlinear Control,1998,8(8):669-686.
|
[1] | SUN Fengqi. State Feedback Generalized H2 Control of Continuous Integrated Control Systems[J]. Applied Mathematics and Mechanics, 2022, 43(8): 901-910. doi: 10.21656/1000-0887.420169 |
[2] | SUN Fengqi. Stability Analysis of Discrete Time-Delay Singularly Perturbed Uncertainty Control Systems[J]. Applied Mathematics and Mechanics, 2021, 42(7): 696-703. doi: 10.21656/1000-0887.410208 |
[3] | TONG Yinghao, TONG Dongbing, CHEN Qiaoyu, ZHOU Wuneng. Design of a Finite-Time State Estimator for Nonlinear Systems Under Event-Triggered Control[J]. Applied Mathematics and Mechanics, 2020, 41(6): 669-678. doi: 10.21656/1000-0887.400210 |
[4] | LI Feng-ming, LIU Chun-chuan. Parametric Vibration Stability and Active Control of Nonlinear Beams[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1284-1293. doi: 10.3879/j.issn.1000-0887.2012.11.004 |
[5] | LIU De-you, ZHANG Jian-hua, GUAN Xin-ping, XIAO Xiao-dan. Generalized LMI-Based Approach to the Global Asymptotic Stability of Cellular Neural Networks With Delay[J]. Applied Mathematics and Mechanics, 2008, 29(6): 735-740. |
[6] | MU Xiao-wu, GUO Xiao-li, CHENG Gui-fang. Adaptive H-infinity Control of a Class of Uncertain Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1056-1064. |
[7] | LI Hai-bin, WANG Zhi-zhen, WANG Long, LI Zhao-ping, LI Er-xiao. Frequency Domain Criteria for Robust D-Stability of MIMO Systems Based on LMI Method[J]. Applied Mathematics and Mechanics, 2006, 27(2): 186-192. |
[8] | SUN Ji-tao, WU Qi-di. Impulsive Control for the Stabilization and Synchronization of Lur’e Systems[J]. Applied Mathematics and Mechanics, 2004, 25(3): 291-296. |
[9] | ZHONG Wan-xie. Variational Method and Computation for H∞ Control[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1271-1278. |
[10] | Zhao Hongyong, Teng Zhidong. On the Absolute Stability of a Class of Inditrect Control Systems[J]. Applied Mathematics and Mechanics, 2000, 21(7): 732-740. |
[11] | Sun Honglie. The High Accuracy Explicit Difference Scheme for Solving Parabolic Equations 3-Dimension[J]. Applied Mathematics and Mechanics, 1999, 20(7): 737-742. |
[12] | Zhu Haiping, Shi Rongchang, Mei Fengxiang. Stability for the Equilibrium State of Chaplygin’s systems[J]. Applied Mathematics and Mechanics, 1995, 16(7): 595-601. |
[13] | Zhang Jiye. Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System[J]. Applied Mathematics and Mechanics, 1995, 16(10): 927-932. |
[14] | Zhang Ji-ye, Shu Zhong-zhou. Necessary and Sufficient Criteria for Absolute Stability of the Direct Control System[J]. Applied Mathematics and Mechanics, 1994, 15(3): 245-251. |
[15] | Qao Guo-cheng. Explicit Criteria of Absolute Stability for the Real Second Canonical Form of Control System[J]. Applied Mathematics and Mechanics, 1993, 14(5): 445-454. |
[16] | Yeh Kai-yuan, Liu Ping. Nonlinear Stability of Spherical Shallow Shell under Compound Loads[J]. Applied Mathematics and Mechanics, 1991, 12(1): 11-17. |
[17] | Zhang Wei. The Criterions for Absolute Stability of Direct Control Systems of Lurie Type[J]. Applied Mathematics and Mechanics, 1989, 10(10): 909-920. |
[18] | Zhao Jun-san. A Criterion for the Stability of Motion of Nonlinear Systems[J]. Applied Mathematics and Mechanics, 1988, 9(11): 1033-1036. |
[19] | Qiu Xiao-gang, Shu Zhong-zhou. Several Criterions of Absolute Stability for the Second Canonical Form of Control System[J]. Applied Mathematics and Mechanics, 1986, 7(9): 785-800. |
[20] | Liao Xiao-xin. On the Criterion for the Absolute Stability of the Control System[J]. Applied Mathematics and Mechanics, 1982, 3(2): 235-248. |