Computing the stability region in delay-space of a TDS using polynomial eigenproblems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 6, Issue PART 1, 2006, Pages 296-301

  Jarlebring, Elias ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Critical delays; Kronecker products; Quadratic eigenproblems; Stability; Stability chart; Time delay systems

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DELAY CONTROL SYSTEMS; SYSTEM STABILITY; TIME DELAY;

CRITICAL DELAYS; EIGEN-PROBLEMS; KRONECKER PRODUCT; STABILITY CHART; TIME-DELAY SYSTEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 79961130762     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20060710-3-it-4901.00049     Document Type: Conference Paper

References (21)

1. Chen, J. and H. Latchman (1995). Frequency sweeping tests for stability independent of delay. IEEE Transactions on automatic control 40(9), 1640-1645.
2. Chen, J., G. Gu and C.N. Nett (1995). A new method for computing delay margins of linear delay systems. Systems and Control Letters 26(2), 107-117.
3. Ergenc, A., N. Olgac and H. Fazelinia (2006). Extended kronecker summation for determining the kernel and offspring of LTI systems with multiple delays. SIAM Journal on Control and Optimization. submitted.
4. Gu, K. and S. Niculescu (2000). Additional dynamics in transformed time-delay systems. IEEE Transactions on automatic control 45(3), 572-575.
5. Gu, K. and S. Niculescu (2005). On stability crossing curves for general systems with two delays. J. Math. Anal. Appl pp. 231-253.
6. Gu, K., V.L. Kharitonov and J. Chen (2003). Stability of time-delay systems. Birkhäuser.
7. Hale, J. (1977). Theory of functional differential equations. Springer-Verlag.
8. Hale, J. (1991). Dynamics and delays. In: Delay differential equations and dynamical systems. pp. 16-30. Lecture notes in mathematics 1475. Springer. Berlin.
9. Hale, J. and W. Huang (1993). Global geometry of the stable regions for two delay differential equations. Journal of Mathematical analysis and applications pp. 344-362.
10. Jarlebring, E. (2006). A quadratic eigenproblem in the analysis of a time delay system. GAMM Annual Meeting, Berlin.
11. Louisell, J. (2001). A matrix method for determining the imaginary axis eigenvalues of a delay system. IEEE Trans. Autom. Control 12, 2008-2012.
12. Mackey, D. S., N. Mackey, C. Mehl and V. Mehrmann (2005). Vector spaces of linearizations of matrix polynomials. SIAM J. of Matrix Analysis and Appl. To appear.
13. Niculescu, S. (2001). Delay effects on stability. A robust control approach.. number 269 In: Lecture notes in control and information sciences. Springer.
14. Niculescu, S., P. Fu and J. Chen (2005). Stability switches and reversals of linear systems with commensurate delays: a matrix pencil characterization. In: IFAC 2005 World Congress, Praha, Czech republic.
15. Nussbaum, R. D. (1978). Differential-delay equations with two time lags. number 205 In: Memoirs of the AMS. Providence.
16. Olgac, N. and R. Sipahi (2002). An exact method for the stability analysis of time-delays linear time-invariant (LTI) systems. IEEE Trans. Aut. Control 47(5), 793-797.
17. Plischke, E. (2005). Transient effects of linear dynamical systems. PhD thesis. Universität Bremen.
18. Sipahi, R. and N. Olgac (2003). Degenerate cases in using the direct method. Journal of Dynamic Systems, Measurement, and Control 125(2), 194-201.
19. Sipahi, R. and N. Olgac (2005a). A comparative survey in determining the imaginary characteristic roots of LTI time delayes systems. In: IFAC 2005 World Congress, Praha, Czech republic.
20. Sipahi, R. and N. Olgac (2005b). Complete stability robustness of third-order LTI multiple time-delay systems. Automatica 41, 1413-1422. (Pubitemid 40774097)
21. Tisseur, K. and F. Meerbergen (2001). The quadratic eigenvalue problem. SIAM Rev 43(2), 235-286.