In this paper, the asymptotic stability for a class of neutral systems with discrete and distributed multiple time delays is considered. Discrete-delay-independent and discrete-delay-dependent criteria are proposed to guarantee stability for such systems. The resulting stability criteria are written in the form of spectral radius and linear matrix inequality (LMI). Some numerical examples are given to illustrate that our obtained results are less conservative.
Issue Section:
Technical Papers
1.
Chen
, J. D.
, Lien
, C. H.
, Fan
, K. K.
, and Cheng
, J. S.
, 2000
, “Delay-Dependent Stability Criterion for Neutral Time-Delays Systems
,” Electron. Lett.
, 36
, pp. 1897
–1898
.2.
Dugard, L., and Verriest, E. I., 1997, Stability and Control of Time-Delay Systems, Springer-Verlag, London.
3.
Fridman
, E.
, 2001
, “New Lyapunov-Krasovskii Functionals for Stability of Linear Retarded and Neutral Type Systems
,” Syst. Control Lett.
, 43
, pp. 309
–319
.4.
Gu
, K.
, Han
, Q. L.
, Luo
, A. C. J.
, and Niculescu
, S. I.
, 2001
, “Discretized Lyapunov Functional for Systems With Distributed Delay and Piecewise Constant Coefficients
,” Int. J. Control
, 74
, pp. 737
–744
.5.
Hale, J. K., and Verduyn Lunel, S. M., 1993, Introduction to Functional Differential Equations, Springer-Verlag, NY.
6.
Hui
, G. Di
, and Hu
, G. Da
, 1997
, “Simple Criteria for Stability of Neutral Systems With Multiple Delays
,” Int. J. Syst. Sci.
, 28
, pp. 1325
–1328
.7.
Ivanescu
, D.
, Dion
, J. M.
, Dugard
, L.
, and Niculescu
, S. I.
, 2000
, “Dynamical Compensation for Time-Delay Systems: An LMI Approach
,” Int. J. Robust Nonlinear Control
, 10
, pp. 611
–628
.8.
Kim
, J. H.
, 2001
, “Delay and its Derivative Dependent Robust Stability of Time-Delayed Linear Systems With Uncertainty
,” IEEE Trans. Autom. Control
, 46
, pp. 789
–792
.9.
Kolmanovskii, V. B., and Myshkis, A., 1999, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic Publ., Dordrecht.
10.
Kolmanovskii
, V. B.
, and Richard
, J. P.
, 1999
, “Stability of Some Linear Systems With Delays
,” IEEE Trans. Autom. Control
, 44
, pp. 984
–989
.11.
Li
, X.
, and de Souza
, C. E.
, 1997
, “Delay-Dependent Robust Stability and Stabilization of Uncertain Linear Delay Systems: A Linear Matrix Inequality Approach
,” IEEE Trans. Autom. Control
, 42
, pp. 1144
–1148
.12.
Lien
, C. H.
, Yu
, K. W.
, and Hsieh
, J. G.
, 2000
, “Stability Conditions for a Class of Neutral Systems With Multiple Time Delays
,” J. Math. Anal. Appl.
, 245
, pp. 20
–27
.13.
Ni, B., and Han, Q. L., 2001, “On Stability for a Class of Neutral Delay-Differential Systems,” Proc. of American Control Conf., Arlington, VA, pp. 25–27.
14.
Niculescu, S. I., 2000, “Further Remarks on Delay-Dependent Stability of Linear Neutral Systems,” Proc. of MTNS 2000, Perpignan, France.
15.
Niculescu, S. I., Neto, T. A., Dion, J. M., and Dugard, L., 1995, “Delay-Dependent Stability of Linear Systems With Delayed State: An LMI Approach,” Proc. of 34th Conf. Decision and Control, New Orleans, LA, Dec., 2, pp. 1495–1496.
16.
Ortega, J. M., 1972, Numerical Analysis, Academic Press, NJ.
17.
Park
, J. H.
, and Won
, S.
, 1999
, “Asymptotic Stability of Neutral Systems With Multiple Delays
,” J. Optim. Theory Appl.
, 103
, pp. 183
–200
.18.
Park
, J. H.
, and Won
, S.
, 2000
, “Stability Analysis for Neutral Delay-Differential Systems
,” J. Franklin Inst.
, 337
, pp. 1
–9
.19.
Park
, P. G.
, 1999
, “A Delay-Dependent Stability Criterion for Systems With Uncertain Time-Invariant Delays
,” IEEE Trans. Autom. Control
, 44
, pp. 876
–877
.20.
Yan
, J. J.
, 2001
, “Robust Stability Analysis of Uncertain Time Delay Systems With Delay-Dependence
,” Electron. Lett.
, 37
, pp. 135
–137
.21.
Juang
, Y. T.
, Kuo
, T. S.
, and Hsu
, C. F.
, 1987
, “Stability Robustness Analysis of Digital Control Systems in State-Space Models
,” Int. J. Control
, 46
, pp. 1547
–1556
.22.
Boyd, S., Ghaoui, L. El, Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia.
23.
Chou
, J. H.
, Chen
, S. H.
, and Li
, J. J.
, 2000
, “Application of the Taguchi-Genetic Method to Design an Optimal Gray-Fuzzy Controller of a Constant Turning Force System
,” J. Mater. Process. Technol.
, 105
, pp. 333
–343
.Copyright © 2003
by ASME
You do not currently have access to this content.
