The asymptotic stability of nonclassically damped systems with nonlinear uncertainties is addressed using the Lyapunov approach. Bounds on nonlinear perturbations that maintain the stability of an asymptotically stable, linear multi-degree-of-freedom system with nonclassical damping are derived. The explicit nature of the construction permits us to directly express the algebraic criteria in terms of plant parameters. The results are then applied to the symmetric output feedback control of multi-degree-of-freedom systems with nonlinear uncertainties. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.
Issue Section:
Technical Papers
1.
Yedavalli
, R. K.
, 1985
, “Perturbation Bounds for Robust Stability in Linear State Space Models
,” Int. J. Control
, 42
(6
), pp. 1507
–1517
.2.
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
.3.
Siljak
, D. D.
, 1989
, “Parameter Space Methods for Robust Control Design: A Guided Tour
,” IEEE Trans. Autom. Control
, 34
(7
), pp. 674
–688
.4.
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
.5.
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
.6.
Hsu
, P.
, and Wu
, J.
, 1991
, “Stability of Second-Order Multidimensional Linear Time-Varying Systems
,” J. Guid. Control Dyn.
, 14
(5
), pp. 1040
–1045
.7.
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
.8.
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
.9.
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.
10.
Skelton, R. E., Iwasaki, T., and Geigoriadis, K., 1998, A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London.
11.
Junkins, J. L., and Kim, Y., 1993, Introduction to Dynamics and Control of Flexible Structures, AIAA, Washington, DC.
Copyright © 2004
by ASME
You do not currently have access to this content.
