Stability analysis for continuous-time positive systems with time-varying delays

IEEE Transactions on Automatic Control

Volumn 55, Issue 4, 2010, Pages 1024-1028

  Liu, Xingwen ^a,b   Yu, Wensheng ^c   Wang, Long ^d  

^a SOUTHWEST UNIVERSITY FOR NATIONALITIES   (China)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c EAST CHINA NORMAL UNIVERSITY   (China)

^d Peking University   (China)

Author keywords

Asymptotic stability; Linear copositive Lyapunov functional; Positive system; Time varying delays

Indexed keywords

COPOSITIVE; LYAPUNOV FUNCTIONALS; POSITIVE SYSTEMS; TIME-VARYING DELAY;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; STABILITY CRITERIA; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

CONTINUOUS TIME SYSTEMS;

EID: 77950791828     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2041982     Document Type: Article

References (35)

1. A. Berman, M. Neumann, and R. J. Stern, Nonnegative Matrices in Dynamic Systems. New York: Wiley, 1989.
2. T. Kaczorek, Positive 1D and 2D Systems. London, U.K.: Springer, 2002.
3. , L. Benvenuti, A. D. Santis, and L. Farina, Eds., Positive Systems, Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer-Verlag, 2003.
4. D. Hinrichsen, N. K. Son, and P. H. A. Ngoc, "Stability radii of higher order positive difference systems," Syst. Control Lett., vol.49, no.5, pp. 377-388, 2003.
5. T. J. Laffey and H. Šmigoc, "Nonnegative realization of spectra having negative real parts," Linear Alg, and Its Applic., vol.416, no.1, pp. 148-159, 2006.
6. Y. Sun, W.Yu, and L.Wang, "Minimal positive realizations for transfer functions with negative poles (in chinese)," in Proc. 25th Chinese Control Conf., Harbin, China, 2006, pp. 90-95.
7. A. Halmschlager and M. Matolcsi, "Minimal positive realizations for a class of transfer functions," IEEE Trans. Circuits Syst. II, vol.52, no.4, pp. 177-180, Apr. 2005.
8. B. Nagy and M. Matolcsi, "A lowerbound on the dimension of positive realizations," IEEE Trans. Circuits Syst. I, vol.50, no.6, pp. 782-784, Jun. 2003.
9. B. D. O. Anderson, M. Deistler, L. Farina, and L. Benvenuti, "Nonnegative realization of a linear system with nonnegative impulse response," IEEE Trans. Circuits Syst. I, vol.43, no.2, pp. 134-142, Feb. 1996.
10. L. Benvenuti and L. Farina, "Positive and compartmental systems," IEEE Trans. Autom. Control, vol.47, no.2, pp. 370-373, Feb. 2002.
11. T. Kaczorek, "Some recent developments in positive 2D systems," in Proc. POSTA, 2003, pp. 345-352.
12. T. Kaczorek, "Stabilization of positive linear systems by state feedback," Pomiary, Automatyka, Kontrola, vol.3, pp. 2-5, 1999.
13. H. Gao, J. Lam, C. Wang, and S. Xu, "Control for stability and positivity: Equivalent conditions and computation," IEEE Trans. Circuits Syst. II, vol.52, no.9, pp. 540-544, Sep. 2005.
14. X. Liu, L.Wang, W. Yu, and S. Zhong, "Constrained control of positive discrete-time systems with delays," IEEE Trans. Circuits Syst. II, vol.55, no.2, pp. 193-197, Feb. 2008.
15. L. Fainshil, M. Margaliot, and P. Chigansky, "On the stability of positive linear switched systems under arbitrary switching laws," IEEE Trans. Autom. Control, vol.54, no.4, pp. 897-899, Apr. 2009.
16. L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications. New York: Wiley, 2000.
17. M. A. Rami and F. Tadeo, "Positive observation problem for linear discrete positive systems," in Proc. 45th IEEE Conf. Decision and Control, CA, 2006, pp. 4729-4733.
18. M. A. Rami and F. Tadeo, "Controller synthesis for positive linear systems with bounded controls," IEEE Trans. Circuits Syst. II, vol.54, no.2, pp. 151-155, Feb. 2007.
19. M. A. Rami, F. Tadeo, and A. Benzaouia, "Control of constrained positive discrete systems," in Proc. 2007 American Control Conf., New York, 2007, pp. 5851-5856.
20. O. Mason and R. Shorten, "The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem," Electron. J. Linear Alg., vol.12, pp. 42-63, 2005.
21. O. Mason and R. Shorten, "On linear copositive Lyapunov functions and the stability of switched positive linear systems," IEEE Trans. Autom. Control, vol.52, no.7, pp. 1346-1349, Jul. 2007.
22. X. Liu, "Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method," IEEE Trans. Circuits Syst. II, vol.56, no.5, pp. 414-418, May 2009.
23. M. A. Rami, U. Helmke, and F. Tadeo, "Positive observation problem for time-delays linear positive systems," in Proc. 15th Mediterranean Conf. Control and Automation, Athens, Greece, 2007, pp. 1-6.
24. W. M. Haddad and V. Chellaboina, "Stability theory for nonnegative and compartmental dynamical systems with time delay," Syst. Control Lett., vol.51, no.5, pp. 355-361, 2004.
25. M. A. Rami, U. Helmke, and F. Tadeo, "Positive observation problem for linear time-lag positive systems," in Proc. 3rd IFAC Symp. Systems, Structure and Control, Foz do Iguaçu, Brazil, 2007.
26. M. Busłowicz, "Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices," Bull. Polish Acad. Sci., Tech. Sci., vol.55, no.1, pp. 1-5, 2007.
27. Z. Shu, J. Lam, H. Gao, B. Du, and L.Wu, "Positive observers and dynamic output-feedback controllers for interval positive linear systems," IEEE Trans. Circuits Syst. I, vol.55, no.10, pp. 3209-3222, Oct. 2008.
28. A. Hmamed, A. Benzaouia, M. A. Rami, and F. Tadeo, "Memoryless control to drive states of delayed continuous-time systems within the nonnegative orthant," in Proc. 17th World Congr., Seoul, Korea, 2008, pp. 3934-3939.
29. X. Liu, "Constrained control of positive systems with delays," IEEE Trans. Autom. Control, vol.54, no.7, pp. 1596-1600, Jul. 2009.
30. A. Hmammed, A. Benzaouia, M. A. Rami, and F. Tadeo, "Positive stabilization of discrete-time systems with unknown delay and bounded controls," in Proc. European Control Conf., Kos, Greece, 2007.
31. E. Fridman and U. Shaked, "An improved stabilization method for linear time-delay systems," IEEE Trans. Autom. Control, vol.47, no.11, pp. 1931-1937, Nov. 2002.
32. Y. Sun, L. Wang, and G. Xie, "Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays," Syst. Control Lett., vol.57, no.2, pp. 175-183, 2008.
33. H.-N. Wu, "Delay-dependent stability analysis and stabilization for discrete-time fuzzy systems with state delay: A fuzzy Lyapunov- Krasovskii functional approach," IEEE Trans. Syst., Man, Cybern. B, vol.36, no.4, pp. 954-962, Aug. 2006.
34. S. Zhou and T. Li, "Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function," Fuzzy Sets & Syst., vol.151, no.1, pp. 139-153, 2005. (Pubitemid 40146245)
35. X. Liu, W. Yu, and L. Wang, "Stability analysis of positive systems with bounded time-varying delays," IEEE Trans. Circuits Syst. II, vol.56, no.7, pp. 600-604, Jul. 2009.