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TECHNICAL PAPERS

Stability Criteria for Nonclassically Damped Systems With Nonlinear Uncertainties

[+] Author and Article Information
D. Q. Cao, Y. M. Ge, Y. R. Yang

Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R. China

J. Appl. Mech 71(5), 632-636 (Nov 09, 2004) (5 pages) doi:10.1115/1.1778719 History: Received July 07, 2003; Revised February 02, 2004; Online November 09, 2004
Copyright © 2004 by ASME
Topics: Stability , Damping , Feedback
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References

Yedavalli,  R. K., 1985, “Perturbation Bounds for Robust Stability in Linear State Space Models,” Int. J. Control, 42(6), pp. 1507–1517.
Zhou,  K. M., and Khargonekar,  P. P., 1987, “Stability Robustness Bounds for Linear State Space Models With Structured Uncertainty,” IEEE Trans. Autom. Control, 32(7), pp. 621–623.
Siljak,  D. D., 1989, “Parameter Space Methods for Robust Control Design: A Guided Tour,” IEEE Trans. Autom. Control, 34(7), pp. 674–688.
Bien,  Z. M., and Kim,  J. H., 1992, “A Robust Stability Bound of Linear Systems With Structured Uncertainty,” IEEE Trans. Autom. Control, 37(10), pp. 1549–1551.
Shieh,  L. S., Mehio,  M. M., and Dib,  H. M., 1987, “Stability of the Second Order Matrix Polynomial,” IEEE Trans. Autom. Control, 32(3), pp. 231–233.
Hsu,  P., and Wu,  J., 1991, “Stability of Second-Order Multidimensional Linear Time-Varying Systems,” J. Guid. Control Dyn., 14(5), pp. 1040–1045.
Cao,  D. Q., and Shu,  Z. Z., 1994, “Robust Stability Bounds for Multi-Degree-of-Freedom Linear Systems With Structured Perturbations,” Dyn. Stab. Syst., 9(1), pp. 79–87.
Diwekar,  A. M., and Yedavalli,  R. K., 1999, “Robust Controller Design for Matrix Second-Order Systems With Structured Uncertainties,” IEEE Trans. Autom. Control, 44(2), pp. 401–405.
Cox, S. J., and Moro, J., “A Lyapunov Function for Systems Whose Linear Part is Almost Classically Damped,” ASME J. Appl. Mech., 64 (4), pp. 965–968.
Skelton, R. E., Iwasaki, T., and Geigoriadis, K., 1998, A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London.
Junkins, J. L., and Kim, Y., 1993, Introduction to Dynamics and Control of Flexible Structures, AIAA, Washington, DC.

Figures

Grahic Jump Location
Schematic of a three-degree-of-freedom vibrator
Grahic Jump Location
Predicted stability regions for the system in Example 1
Grahic Jump Location
Predicted stability regions for the system in Example 2

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