Robust stabilization and H ∈∞∈ control of uncertain distributed delay systems

Lecture Notes in Control and Information Sciences

Volumn 388, Issue , 2009, Pages 221-231

  Münz, Ulrich ^a   Rieber, Jochen M ^b   Allgöwer, Frank ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

^b AIRBUS DEFENCE AND SPACE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROLLER SYNTHESIS; DISTRIBUTED DELAYS; FULL-BLOCK S-PROCEDURE; LINEAR FRACTIONAL FORMS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MATRIX; MATRIX INEQUALITY; RATIONAL FUNCTION; ROBUST H; ROBUST STABILIZATION; SYNTHESIS CONDITIONS; SYSTEM MATRICES; UNCERTAIN LINEAR SYSTEM;

FUNCTION EVALUATION; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; ROBUST CONTROL; ROBUSTNESS (CONTROL SYSTEMS); STABILIZATION; UNCERTAIN SYSTEMS;

DELAY CONTROL SYSTEMS;

EID: 70349902416     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-02897-7_19     Document Type: Conference Paper

References (41)

1. Baker, G.A.: Essentials of Padé Approximants. Academic Press, New York (1975)
2. Bernard, S., Bélair, J., Mackey, M.C.: Sufficient conditions for stability of linear differential equations with distributed delay. Discrete and Continuous Dynamical Systems - Series B 1, 233-256 (2001)
3. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in systems and control theory. SIAM, Philadelphia (1994)
4. Breda, D., Maset, S., Vermiglio, R.: Pseudospectral differencing methods for characteristic roots of delay differential equations. SIAM J. Scientific Computing 27(2), 482-495 (2005)
5. Chen, W.H., Zheng, W.X.: Delay-dependent robust stabilization for uncertain neutral systems with distributed delays. Automatica 43(1), 95-104 (2007)
6. Cushing, J.M.: Integrodifferential equations and delay models in population dynamics. Springer, Heidelberg (1977)
7. Fiagbedzi, Y.A., Pearson, A.E.:A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica 23(3), 311-326 (1987)
8. Fridman, E., Tsodik, G.: H? control of systems with distributed delay: Discretized Lyapunov functional method. In: Proc. European Control Conf., Kos, Greece, pp. 229-234 (2007)
9. Gopalsamy, K.: Global asymptotic stability in volterra's population systems. J. Math. Bio. 19, 157-168 (1984)
10. Gu, K., Han, Q.L., Luo, A.C.J., Niculescu, S.I.: Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficients. Int. J. Contr. 74(7), 737-744 (2001)
11. Gu, K., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Birkhäuser, Boston (2003)
12. Gu, K.: An improved stability criterion for systems with distributed delays. Int. J. Robust and Nonlinear Control 13(9), 819-831 (2003)
13. Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, Heidelberg (1993)
14. Han, Q.L.: A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica 40(10), 1791-1796 (2004)
15. Iwasaki, T., Shibata, G.: LPV system analysis via quadratic separator for uncertain implicit systems. IEEE Trans. Autom. Contr. 46(8), 1195-1208 (2001)
16. Kharitonov, V.L.: Lyapunov matrices for a class of time-delay systems. Systems & Control Letters 55(7), 610-617 (2006)
17. Kolmanovskii, V.B., Richard, J.P.: Stability of some linear systems with delays. IEEE Trans. Autom. Contr. 44(5), 984-989 (1999)
18. Li, X.G., Zhu, X.J.: Stability analysis of neutral systems with distributed delays. Automatica 44(8), 2197-2201 (2008)
19. MacDonald, N.: Biological delay systems: linear stability theory. Cambridge University Press, Cambridge (1989)
20. Michiels, W., Van Assche, V., Niculescu, S.I.: Stabilization of time-delay systems with a controlled time-varying delay and applications. IEEE Trans. Autom Contr. 50(2), 493-504 (2005)
21. Michiels, W., Morarescu, I.C., Niculescu, S.I.: Consensus problems for car following systems with distributed delays. In: Proc. European Control Conf., Kos, Greece, pp. 2158-2165 (2007)
22. Morarescu, I.C., Niculescu, S.I., Gu, K.: Stability crossing curves of shifted gammadistributed delay systems. SIAM J. Applied Dynamical Systems 6(2), 475-493 (2007)
23. Münz, U., Rieber, J.M., Allgöwer, F.: Robust stability of distributed delay systems. In: Proc. 17th IFAC World Congress, Seoul, South Korea, pp. 12354-12358 (2008)
24. Münz, U., Allgöwer, F.: L2-gain based controller design for linear systems with distributed delays and rational delay kernels. In: Proc. 7th IFAC Workshop on Time-Delay Systems, Nantes, France (2007)
25. Niculescu, S.I.: Delay effects on stability: A robust control approach. Springer, Heidelberg (2001)
26. Niculescu, S.I., Gu, K. (eds.): Advances in time-delay systems. Springer, Heidelberg (2004)
27. Richard, J.P.: Time-delay systems: An overview of some recent advances and open problems. Automatica 39(10), 1667-1694 (2003)
28. Roesch, O., Roth, H., Niculescu, S.I.: Remote control of mechatronic systems over communication networks. In: Proc. Int. Conf. on Mechatronics and Automation, Niagara Falls, Canada, pp. 1648-1653 (2005)
29. Santos, O., Mondié, S., Kharitonov, V.L.: Robust stability conditions for systems with distributed delays. In: Proc. IEEE Conf. Decision and Control, San Diego, USA, pp. 217-222 (2006)
30. Scherer, C.W., Weiland, S.: Linear matrix inequalities in control (2005), http://www.cs.ele.tue.nl/sweiland/lmi.html
31. Scherer, C.W.: Robust mixed control and linear parameter-varying control with full block multipliers. In: EL Ghaoui, L., Niculescu, S.I. (eds.) Recent Advances on LMI Methods in Control. SIAM, Philadelphia (2000)
32. Scherer, C.W.: LPV control and full block multipliers. Automatica 37(3), 361-375 (2001)
33. Scherer, C.W.: LMI relaxations in robust control. Europ. J. Contr. 12(1), 3-29 (2006)
34. de Souza, C.E., Li, X.: Delay-dependent robust H-infinity control of uncertain linear state-delayed systems. Automatica 35(7), 1313-1321 (1999)
35. van der Schaft, A.: L2-gain and passivity techniques in nonlinear control. Springer, Heidelberg (1996)
36. Verriest, E.I.: Linear systems with rational distributed delay: Reduction and stability. In: Proc. European Control Conf., Karlsruhe, Germany (1999)
37. Xie, L., Fridman, E., Shaked, U.: Robust H? control of distributed delay systems with application to combustion control. IEEE Trans. Autom. Contr. 46(12), 1930-1935 (2001)
38. Yue, D., Han, Q.L.: RobustH? filter design of uncertain descriptor systems with discrete and distributed delays. In: Proc. IEEE Conf. Decision and Control, Maui, USA, pp. 610- 615 (2003)
39. Zheng, F., Cheng, M., Gao, W.B.: Feedback stabilization of linear systems with distributed delays in state and control variables. IEEE Trans. Autom. Contr. 39(8), 1714-1718 (1994)
40. Zheng, F., Frank, P.M.: Finite dimensional variable structure control design for distributed delay systems. Int. J. Contr. 74(4), 398-408 (2001)
41. Zheng, F., Frank, P.M.: Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica 38(2), 487-497 (2002)