Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 56, Issue 5, 2009, Pages 414-418

  Liu, Xingwen ^a,b  

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

^b SOUTHWEST UNIVERSITY FOR NATIONALITIES   (China)

Author keywords

Linear programming (LP); Stability; Switched linear copositive Lyapunov function (SLCLF); Switched linear positive system (SLPS)

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LINEAR PROGRAMMING; LYAPUNOV FUNCTIONS; STABILITY CRITERIA;

COMMON LINEAR CO-POSITIVE LYAPUNOV FUNCTIONS; COPOSITIVE; DISCRETE TIME; LYAPUNOV FUNCTION METHOD; POSITIVE SYSTEMS; STABILITY ANALYSIS; STABILITY PROBLEM;

SYSTEM STABILITY;

EID: 67349220777     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2009.2019326     Document Type: Article

References (32)

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-Verlag, 2002.
3. J. M. van Den, "Positive linear observers for linear compartmental systems," SIAM J. Control Optim., vol. 36, no. 2, pp. 590-608, Mar. 1998.
4. L. Benvenuti and L. Farina, "Positive and compartmental systems," IEEE Trans. Autom. Control, vol. 47, no. 2, pp. 370-373, Feb. 2002.
5. L. Benvenuti and L. Farina, "A tutorial on the positive realization problem," IEEE Trans. Autom. Control, vol. 49, no. 5, pp. 651-664, May 2004.
6. R. Shorten, D. Leith, J. Foy, and R. Kilduff, "Towards an analysis and design framework for congestion control in communication networks," in Proc. 12th Yale Workshop Adaptive Learning Syst., 2003.
7. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988-1001, Jun. 2003
8. T. Kaczorek, "The choice of the forms of Lyapunov functions for a positive 2D Roesser model," Int. J. Appl. Math. Comput. Sci., vol. 17, no. 4, pp. 471-475, Dec. 2007.
9. T. Kaczorek, "A realization problem for positive continuous-time systems with reduced numbers of delays," Int. J. Appl.Math. Comput. Sci., vol. 16, no. 3, pp. 325-331, 2006.
10. L. Benvenuti, A. D. Santis, and L. Farina, Eds., Positive Systems, Lecture Notes in Control and Information Sciences, vol. 294. Berlin, Germany: Springer-Verlag, 2003.
11. M. A. Rami, F. Tadeo, and A. Benzaouia, "Control of constrained positive discrete systems," in Proc. Amer. Control Conf., New York, 2007, pp. 5851-5856.
12. M. A. Rami and F. Tadeo, "Positive observation problem for linear discrete positive systems," in Proc. 45th IEEE Conf. Decision Control, San Diego, CA, 2006, pp. 4729-4733.
13. 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, Apr. 2004.
14. M. A. Rami, U. Helmke, and F. Tadeo, "Positive observation problem for time-delays linear positive systems," in Proc. 15th Mediterranean Conf. Control Autom., Athens, Greece, 2007, pp. 1-6.
15. L. Gurvits, R. Shorten, and O. Mason, "On the stability of switched positive linear systems," IEEE Trans. Autom. Control, vol. 52, no. 6, pp. 1099-1103, Jun. 2007.
16. O. Mason and R. Shorten, "The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem," Electron. J. Linear Algebra, vol. 12, pp. 42-63, 2005.
17. 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.
18. O. Mason and R. Shorten, "Some results on the stability of positive switched linear systems," in 43rd IEEE Conf. Decision Control, 2004, pp. 4601-4606.
19. O. Mason and R. Shorten, "Quadratic and copositive Lyapunov functions and the stability of positive switched linear systems," in Proc. Amer. Control Conf., 2007, pp. 657-662.
20. S. Chaib, D. Boutat, A. Benali, and F. Kratz, "Dynamic controller of switched linear systems: A common Lyapunov function approach," in Proc. 45th IEEE Conf. Decision Control, 2006, pp. 125-130.
21. R. Shorten, K. S. Narendra, and O. Mason, "A result on common quadratic Lyapunov functions," IEEE Trans. Autom. Control, vol. 48, no. 1, pp. 110-113, Jan. 2003.
22. M. S. Branicky, "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 475-482, Apr. 1998.
23. D. Liberzon and A. S. Morse, "Basic problems in stability and design of switched systems," IEEE Control Syst. Mag., vol. 19, no. 5, pp. 59-70, Oct. 1999.
24. J. Daafouz, P. Riedinger, and C. Iung, "Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach," IEEE Trans. Autom. Control, vol. 47, no. 11, pp. 1883-1887, Nov. 2002.
25. G. Xie and L.Wang, "Quadratic stability and stabilization of discrete-time switched systems with state delay," in 43rd IEEE Conf. Decis. Control, 2004, pp. 3235-3240.
26. H. Gao, L. Zhang, P. Shi, S. Mou, and C.Wang, "Stability and stabilization of switched linear discrete-time systems with polytopic uncertainties," in Proc. Amer. Control Conf., 2006, pp. 5953-5958.
27. Y. G. Sun, L. Wang, and G. Xie, "Stability of switched systems with time-varying delays: Delay-dependent common Lyapunov functional approach," in Proc. Amer. Control Conf., 2006, pp. 1544-1549.
28. D. Du, B. Jiang, P. Shi, and S. Zhou, "H∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach," IEEE Trans. Autom. Control, vol. 52, no. 8, pp. 1520-1525, Aug. 2007.
29. L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications. New York: Wiley, 2000.
30. M. Vidyasagar, Nonlinear Systems Analysis, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1992.
31. T. Coleman,M. Branch, and A. Grace, Optimization Toolbox for Use With Matlab. Natick, MA: MathWorks Inc., 1999.
32. S. Boyd, E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.