On the estimation of eigenvalue regions for discrete time-delay systems with a class of highly structured perturbations
Article
Received:
Accepted:
- 62 Downloads
- 1 Citations
Abstract
By means of norm,M-matrix, and matrix measure techniques, this paper estimates several restricted regions in the complex plane in which all eigenvalues of a class of discrete time-delay systems subjected to highly structured parametric perturbations are located. Both the stability and the instability conditions for these systems are also investigated via the proposed schemes. Two numerical examples are given to verify the correctness and demonstrate the applicability of the quantitative results.
Keywords
Measure Technique Complex Plane Quantitative Result Parametric Perturbation Instability Condition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [1]A. A. Abdul-Wahab, Perturbation bounds for root-clustering of linear discrete-time systems,Int. J. Systems Sci.,22, 1991, 1775–1783.Google Scholar
- [2]M. Araki,M-matrices and their applications, II,Syst. Control (in Japanese),37, 1977, 114–121.Google Scholar
- [3]M. Araki, Stability of large-scale nonlinear systems — Quadratic-order theory of composite-system method usingM-matrices,IEEE Trans. Automat. Control,23, 1978, 129–142.Google Scholar
- [4]B. R. Barmish, A generalization of Kharitonov's four-polynomial concept for robust stability problem with linear dependent coefficient perturbations,IEEE Trans. Automat. Control,34, 1989, 157–165.Google Scholar
- [5]J. H. Chou, Robustness of pole-assignment in specified circular region for linear perturbed systems,Syst. Control Lett.,16, 1991, 41–44.Google Scholar
- [6]J. H. Chou, S. J. Ho, and I. R. Horng, Robustness of disk-stability for perturbed large-scale systems,Automatica,28, 1992, 1063–1066.Google Scholar
- [7]S. Gutman and E. I. Jury, A general theory for matrix root-clustering in subregions of the complex plane,IEEE Trans. Automat. Control,26, 1981, 853–862.Google Scholar
- [8]S. Gutman and H. Taub, Linear matrix equations and root clustering,Int. J. Control,50, 1989, 1635–1643.Google Scholar
- [9]H. Y. Horng, J. H. Chou, and I. R. Horng, Robustness of eigenvalue clustering in various regions of the complex plane for perturbed systems,Int. J. Control,57, 1993, 1469–1484.Google Scholar
- [10]I. R. Horng, H. Y. Horng, and J. H. Chou, Eigenvalue clustering in subregions of the complex plane for interval dynamic systems,Int. J. Systems Sci.,24, 1993, 901–914.Google Scholar
- [11]Y. T. Juang, Robust stability and robust pole assignment of linear systems with structured uncertainty,IEEE Trans. Automat. Control,36, 1991, 635–637.Google Scholar
- [12]P. Lancaster,The Theory of Matrices, Academic Press, New York, 1985.Google Scholar
- [13]C. H. Lee, T.-H. S. Li, and F. C. Kung, D-stability analysis for discrete systems with a time delay,Syst. Control Lett.,19, 1992, 213–219.Google Scholar
- [14]T. Mori, T. Fukuma, and M. Kuwahara, Delay independent stability criteria for discrete-delay systems,IEEE Trans. Automat. Control,27, 1982, 964–966.Google Scholar
- [15]A. Richid, Robustness of pole assignment in a specified region for perturbed systems,Int. J. Systems Sci.,21, 1990, 579–585.Google Scholar
- [16]M. G. Singh and H. Tamura, Modeling and hierarchical optimization for oversaturated urban road traffic networks,Int. J. Control,20, 1974, 913–934.Google Scholar
- [17]C. B. Soh, C. S. Berger, and K. P. Dabke, Addendum to: On the stability properties of polynomials with perturbed coefficients,IEEE Trans. Automat. Control,32, 1987, 230–240.Google Scholar
- [18]T. T. Su and W. J. Shyr, Robust D-stability for linear uncertain discrete time-delay systems,IEEE Trans. Automat. Control,39, 1994, 425–428.Google Scholar
- [19]H. Tamura, A discrete dynamic model with distributed transport delays and its hierarchical optimization for preserving stream quality,IEEE Trans. Syst. Man. Cybern.,4, 1974, 424–431.Google Scholar
- [20]H. Tamura, Decentralized optimization for distributed lag models of discrete systems,Automatica,11, 1975, 593–602.Google Scholar
- [21]A. Vicino, Robustness of pole location in perturbed systems,Automatica,25, 1989, 109–113.Google Scholar
- [22]M. Vidyasagar,Nonlinear Systems Analysis, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ, 1993.Google Scholar
- [23]S. S. Wang and W. G. Lin, On the analysis of eigenvalue assignment robustness,IEEE Trans. Automat. Control,37, 1992, 1561–1564.Google Scholar
- [24]R. K. Yedavalli, Robust root clustering for linear uncertain systems using generalized Lyapunov theory,Automatica,29, 1993, 237–240.Google Scholar
- [25]M. M. Zavarei and M. Jamshidi,Time-Delay Systems Analysis, Optimization and Applications, Elsevier, North-Holland, Amsterdam, 1987.Google Scholar
Copyright information
© Birkhäuser 1996