Extended Kronecker summation for determining the kernel and offspring of LTI systems with multiple delays

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 6, Issue PART 1, 2006, Pages 157-162

  Ergenc, Ali Fuat ^a   Olgac, Nejat ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Kronecker sum; Stability; Time delay system

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DELAY CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; TIME DELAY;

CHARACTERISTIC ROOTS; CLUSTER TREATMENT OF CHARACTERISTIC ROOTS; COMPUTATIONAL TIME; EIGENVALUE PROBLEM; FINITE DIMENSIONAL; INFINITE DIMENSIONAL; KRONECKER; TIME-DELAY SYSTEMS;

LINEAR SYSTEMS;

EID: 79961164936     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20060710-3-it-4901.00026     Document Type: Conference Paper

References (23)

1. Bernstein, D. S. (2005). Matrix Mathematics, Princeton University Press.
2. Brewer, J. W. (1978). "Kronecker products and matrix calculus in system theory." IEEE Transactions on Circuits and Systems CAS-25: 772-781.
3. Campbell, S. A. (1999). "Stability and Bifurcation of a Simple Neural Network with Multiple Time Delays." Fields Institute Communications 21: 65-79.
4. Chapellat, H. and Bhattacharyya, S. P. (1989). "A Generalization of Kharitonov's Theorem: Robust Stability of Interval Plants." IEEE Transactions on Automatic Control 34(3): 306-311.
5. Chen, J., Gu, G. and Nett, C. N. (1995). "A new method for computing delay margins for stability of linear delay systems." Systems & Control Letters 26: 107-117.
6. El'sgol'ts, L. E. and Norkin, S. B. (1973). Introductionto the Theory and Application of Differential Equations with Deviating Arguments. New York, Academic Press.
7. Fazelinia, H., Sipahi, R. and Olgac, N. (2005). Stability Analysis of Multiple Time Delayed Systems Using 'Building Block' Concept, Alarm Lab http://www.engr.uconn.edu/alarm/reports.htm.
8. Fu, M., Olbrot, A. W. and Polis, M. P. (1989). "Robust stability for time-delayed systems: The edge theorem and graphical tests." IEEE Transactions on Automatic Control 34(8): 813-819.
9. Hale, J. K. (1977). Theory of Functional Differential Equations. New York, Springer-Verlag.
10. Hale, J. K. and Huang, W. (1993). "Global Geometry of the Stable Regions for Two Delay Differential Equations." Journal of Mathematical Analysis and Applications 178: 344-362.
11. Hale, J. K. and Verduyn Lunel, S. M. (1993). An Introduction to Functional Differential Equations. New York, Springer-Verlag.
12. Jarlebring, E. (2005). Computing Critical Delays fo Time Delay Systems using Polynomial Eigenproblems, http://www-public.tu-bs.de:8080/~jarlebri/ publications.html.
13. Kamen, E. W. (1982). "Linear Systems with Commensurate Time Delays: Stability and Stabilization Independent of Delay." IEEE Transactions on Automatic Control 25(2): 367-375.
14. Kharitonov, V. L. and Zhabko, A. P. (1994). "Robust Stability of Time-Delay Systems." IEEE Transactions on Automatic Control 39(12): 2388-2397.
15. Nussbaum, R. (1978). Differential delay equations with two time lags.
16. Olgac, N. and Sipahi, R. (2002). "An exact method for the stability analysis of time delayed LTI systems." IEEE Transactions on Automatic Control 47(5): 793-797. (Pubitemid 34692263)
17. Richard, J. P. (2003). "Time-Delay systems: an overview of some recent advances and open problems." Automatica 39: 1667-1694.
18. Silva, G. J., Datta, A. and Bhattacharyya, S. P. (2001). "PI Stabilization of first-order systems with time delay." Automatica 37: 2025-2031. (Pubitemid 32951300)
19. Sipahi, R., Fazelinia, H. and Olgac, N. (2005). Generalization of Cluster Treatment of Characteristic Roots for Robust Stability of Multiple Time Delayed Systems, Alarm Lab http://www.engr.uconn.edu/alarm/reports.htm.
20. Sipahi, R. and Olgac, N. (2004). A Novel Stability Study on Multiple Time-Delay Systems (MTDS) Using the Root Clustering Paradigm. Boston, MA.
21. Sipahi, R. and Olgac, N. (2005). "Complete stability robustness of third-order LTI multiple time-delay systems." Automatica 41(9): 1413-1422. (Pubitemid 40774097)
22. Stepan, G. (1989). Retarded Dynamical Systems: Stability and Characteristic Function. New York, Longman Scientific & Technical,co- publisher John Wiley & Sons Inc., US.
23. Su, J.-H. (1995). "The Asymptotic Stability of Linear Autonomous Systems with Commensurate Time Delays." IEEE Transactions on Automatic Control 40: 1114-1117.