Stabilization of linear uncertain delay systems with antisymmetric stepwise configurations

Journal of Dynamical and Control Systems

Volumn 14, Issue 1, 2008, Pages 1-31

  Hashimoto, T ^a   Amemiya, T ^b   Fujii, H A ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

^b SETSUNAN UNIVERSITY   (Japan)

Author keywords

M matrix; Robust control; Stabilization; Time delay; Uncertain system

Indexed keywords

ANTISYMMETRIC STEPWISE CONFIGURATIONS; LINEAR UNCERTAIN DELAY SYSTEMS; M-MATRIX;

CONTROL SYSTEM STABILITY; DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; ROBUST CONTROL; TIME DELAY;

UNCERTAIN SYSTEMS;

EID: 37449018419     PISSN: 10792724     EISSN: 15738698     Source Type: Journal    
DOI: 10.1007/s10883-007-9035-3     Document Type: Article

References (22)

1. T. Amemiya, Development of the conditions for the delay independent stabilization of uncertain linear delayed systems. Trans. Inst. Systems Control Inform Engrs. 9 (1996), 252-254 (in Japanese).
2. T. Amemiya and G. Leitmann, A method for designing a stabilizing control for a class of uncertain linear delay systems. Dynam. Control 4 (1994), 147-167.
3. B. R. Barmish, Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. J. Optim. Theory Appl. 46 (1985), 399-408.
4. ∞ control problems. IEEE Trans. Automat. Control 34 (1989), 831-847.
5. M. Fiedler and V. Pták, On matrices with non-positive off-diagonal elements and positive principal minors. Czechoslovak Math. J. 12 (1962), 382-400.
6. E. Fridman and U. Shaked, Parameter dependent stability and stabilization of uncertain time-delay systems. IEEE Trans. Automat. Control 48 (2003), 861-866.
7. K. Gu, V. L. Kharitonov, and J. Chen, Stability of time-delay systems. Birkhäuser (2003).
8. A. Halanay, Differential equations. Academic Press (1966).
9. J. Hale, Theory of functional differential equations. Springer-Verlag (1977).
10. ∞ control theory. IEEE Trans. Automat. Control 35 (1990), 356-361.
11. N. N. Krasovkii, Stability of motion. Stanford Univ. Press (1963).
12. V. Lakshmikantham and S. Leera, Differential and integral inequalities. Academic Press (1969).
13. G. Leitmann, Guaranteed asymptotic stability for some linear systems with bounded uncertainties. J. Dynam. Syst. Meas. Contr. 101 (1979), 212-216.
14. M. S. Mahmoud and N. F. AI-Muthairi, Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties. IEEE Trans. Automat. Control 39 (1994), 2135-2139.
15. C. D. Meyer, Matrix analysis and applied linear algebra. Soc. Industr. Appl. Math. (2001).
16. ∞ memoryless control with α-stability constraint for time-delay systems: An LMI approach. IEEE Trans. Automat. Control 43 (1998), 739-743.
17. S.-I. Niculescu and K. Gu, Advances in time-delay systems. Lect. Notes Comput. Sci. Engineering 38, Springer-Verlag (2004).
18. J. M. Ortega and W. C. Rheinholdt, Iterative solution of nonlinear equations in several variables. Academic Press (1970).
19. I. R. Petersen, Structural stabilization of uncertain systems: Necessity of the matching condition. SIAM J. Control Optim. 23 (1985), 286-296.
20. J.-P. Richard, Time-delay systems: An overview of some recent advances and open problems. Automatica 39 (2003), 1667-1694.
21. K. Wei, Quadratic stabilizability of linear systems with structural independent time-varying uncertainties. IEEE Trans. Automat. Control 35 (1990), 268-277.
22. K. Wei, Stabilization of linear time-invariant interval systems via constant state feedback control. IEEE Trans. Automat. Control 39 (1994), 22-32.