Easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems

Systems and Control Letters

Volumn 57, Issue 2, 2008, Pages 165-174

  Wei, Ping ^a,b   Guan, Qiang ^a   Yu, Wensheng ^a,d   Wang, Long ^c  

^a INSTITUTE OF AUTOMATION   (China)

^b CHINA UNIVERSITY OF PETROLEUM   (China)

^c PEKING UNIVERSITY   (China)

^d TSINGHUA UNIVERSITY   (China)

Author keywords

Algebraic criteria; Complete discrimination system for polynomials; Delay bound; Delay independent stability; Global hyperbolicity; Neutral dynamical systems

Indexed keywords

DISCRIMINATORS; EIGENVALUES AND EIGENFUNCTIONS; NUMERICAL METHODS; POLYNOMIALS;

DELAY BOUND; DELAY-INDEPENDENT STABILITY; GLOBAL HYPERBOLICITY; NEUTRAL DYNAMICAL SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 37049017138     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2007.08.012     Document Type: Article

References (30)

1. Avellar C.E., and Hale J.K. On the zeros of exponential polynomials. J. Math. Anal. Appl. 73 (1980) 434-452
2. Bellman R., and Cooke K.L. Differential-Difference Equations (1963), Academic Press, New York
3. Boukas E.K., and Liu Z.K. Deterministic and Stochastic Time Delay System (2002), Birkhäuser, Boston, Basel, Berlin
4. Brumley W.E. On the asymptotic behavior of solutions of differential-difference equations of neutral type. J. Differential Equations 7 (1970) 175-188
5. Chen J., and Latchman H.A. Frequency sweeping tests for stability independent of delay. IEEE Trans. Automat. Contr. AC-40 (1995) 1640-1645
6. Gantmacher F. The Theory of Matrices (1959), Chelsea, New York
7. Gu N., Tan M., and Yu W.S. An algebra test for unconditional stability of linear delay systems. Proceedings of the 40th IEEE Conference on Decision and Control (CDC 2001) (2001), Orlando, Florida, USA 4746-4747
8. Hale J.K. Theory of Functional Differential Equations (1977), Springer, New York
9. Hale J.K., Infante E.F., and Tsen F.-S.P. Stability in linear delay equations. J. Math. Anal. Appl. 105 (1985) 533-555
10. Hale J.K., and Verduyn Lunel S.M. Introduction to Functional Differential Equations (1993), Springer, New York
11. Han Q.-L. On delay-dependent stability for neutral delay-differential systems. Internat. J. Appl. Math. Comput. Sci. 11 (2001) 965-976
12. Hertz D., Jury E.J., and Zeheb E. Stability independent and dependent of delay for delay differential systems. J. Franklin Inst. 318 (1984) 143-150
13. Hu G.Di., and Hu G.Da. Some simple stability criteria of neutral delay-differential systems. Appl. Math. Comput. 80 (1996) 257-271
14. Kamen E.W. Linear systems with commensurate time-delays: stability and stabilization independent of delay. IEEE Trans. Automat. Contr. AC-27 (1982) 367-375
15. Kharitonov V.L. Robust stability analysis of time delay systems: a survey. Annual Rev. Contr. 23 (1999) 185-196
16. V.L. Kharitonov, J.A Torres-Muñoz, M.B. Ortiz-Moctezuma, Polytopic families of quasi-polynomials: vertex-type stability conditions, IEEE Trans. Circuits Syst. Part I CAS-50 (2003) 1413-1420.
17. Kharitonov V.L., and Zhabko A.P. Robust stability of time-delay systems. IEEE Trans. Automat. Contr. AC-39 (1994) 2388-2397
18. Khusainov D.Ya., and Yun'kova E.V. Investigation of the stability of linear systems of neutral type by the Lyapunov function method. Differential'nye Uravneriya 24 (1988) 613-621
19. Li M.L. Stability of linear neutral delay-differential systems. Bull. Austral. Math. Soc. 38 (1988) 339-344
20. Park J.-H., and Won S. Stability analysis for neutral delay-differential systems. J. Franklin Inst. 337 (2000) 1-9
21. Qin Y.X., Liu Y.Q., Wang L., and Zheng Z.X. Stability of Dynamical Systems with Delays. second ed. (1989), Science Press, Beijing
22. Ren H.S., and Li H.Y. Explicit asymptotic stability criteria for neutral differential equations with two delays. Appl. Math. E Notes 2 (2002) 1-9
23. Ren H.S., and Zheng Z.X. Algebraic criterion for asymptotic stability of neutral equations of the form over(x, ̇) (t) + c over(x, ̇) (t - τ) + ax (t) + bx (t - τ) = 0. Acta. Math. Sinica 42 6 (1999) 1077-1088
24. Verriest E.I., and Niculescu S.I. Delay-independent stability of linear neutral systems: a Riccati equation approach. In: Dugard L., and Verriest E.I. (Eds). Stability and Control of Time-Delay Systems (1997), Springer, London 92-100
25. Wang Z.D., Lam J., and Burnham K.J. Stability analysis and observer design for neutral delay systems. IEEE Trans. Automat. Contr. AC-47 (2002) 478-483
26. Wu J.Y. The position of boundary surface for a sort of trancendental equation with three parameters. Acta. Math. Sinica 37 (1994) 301-308
27. Yang L. Recent advances on determining the number of real roots of parametric polynomials. J. Symbolic Comput. 28 (1999) 225-242
28. Yang L., Hou X.R., and Zeng Z.B. A complete discrimination system for polynomials. Sci. China E-39 (1996) 628-646
29. Yang L., Zhang J., and Hou X. Nonlinear Algebraic Equations and Machine Proving (1996), Shanghai Science and Education Press, Shanghai
30. k x (t - k τ), in: Chinese Control Conference (CCC2000), Hong Kong, 2000, pp. 435-439.