The time-varying gap and coprime factor perturbations
Tóm tắt
The connection between the time-varying gap metric and two-block problems is utilized to obtain criteria for robust stabilization of linear, discretetime, time-varying systems. In particular we give a formula for the optimal minimal angle for a stabilizable linear time-varying system and show that it has a maximally stabilizing controller.
Tài liệu tham khảo
W. Dale and M. Smith, Stabilizability and existence of system representations for discrete-time time-varying systems,SIAM J. Control Optim. 31(6) (1993), 1538–1557.
K. Davidson,Nest Algebras, Pitman Research Notes in Mathematics, Vol. 191, Longman, London, 1988.
A. El-Sakkary, The gap metric: robustness of stabilization of feedback systems,IEEE Trans. Automat. Control 30 (1985), 240–247.
A. Feintuch, The gap metric for time-varying systems,Systems Control Lett. 16 (1991), 277–279.
A. Feintuch, Graphs of linear time-varying systems and coprime factorizations,J. Math. Anal. Appl. 163(1) (1992), 79–85.
A. Feintuch, Robustness of time-varying systems,MCSS 6 (1993), 247–263.
A. Feintuch, Gap metric robustness for linear time-varying systems,Linear Algebra Appl.,208 (1994), 209–221.
A. Feintuch and B. Francis, Uniformly optimal control of linear time-varying systems,Systems Control Lett. 5 (1984), 67–71.
A. Feintuch and R. Saeks,System Theory: A Hilbert Space Approach, Academic Press, New York, 1982.
C. Foias, T. Georgiou, and M. Smith, Robust stability of feedback systems: a geometric approach using the gap metric,SIAM J. Control Optim. 31(6) (1993), 1518–1537.
T. Georgiou, On the computation of the gap metric,Systems Control Lett. 11 (1988), 253–257.
T. Georgiou, and M. Smith, Optimal robustness in the gap metric,IEEE Trans. Automat. Control 35 (1990), 673–686.
M. A. Krasnosel'skiiet al., Approximate Solutions of Operator Equations, Wolters-Noordhoff, Groningen, 1972.
N. Nikolskii,Treatise on the Shift Operator, Springer-Verlag, Berlin, 1986.
R. Ober and J. Sefton, Stability of control systems and graphs of linear systems,Systems Control Lett. 17 (1991), 265–280.
R. Ober and J. Sefton, On the gap metric and coprime factor pertubations,Automatica,29(3) (1993), 723–734.
L. Qui and E. Davison, Feedback stability under simultaneous gap metric uncertainities in plant and controller,Systems Control Lett. 18 (1992), 9–22.
M. Vidyasagar,Control System Synthesis: A Factorization Approach, MIT Press, Cambridge, MA, 1985.
M. Vidyasagar and H. Kimura, Robust stabilization for uncertain linear multivariable systems,Automatica 22 (1986), 85–94.
S. Zhu, Robustness of feedback stabilization: A topological approach, Ph.D. thesis, Eindhoven, 1989.
S. Zhu, M. Hautus, and C. Pragman, Sufficient conditions for robust BIBO stabilization: given by the gap metric,Systems Control Lett. 11 (1988), 53–59.