臺灣博碩士論文加值系統

此篇論文我們探討二階系統輸出回授可被正則化的條件,我們知道在成比例和微分的輸出回授控制條件下,會形成一個封閉系統且此封閉系統是正則化且指標小於等於1. 這些性質敘述動力代數方程系統可解性.

Conditions are given under which a second-order system can be regularized
by output feedback. It is shown that under these conditions, proportional
and derivative output feedback controls can be constructed such that
the closed-loop system is regular and has index at most one. This property
ensures the solvability of the resulting system of dynamic-algebraic equations.
A reduced form is given that allows the system procedures used to
establish the theory are based only on orthogonal matrix decompositions
and can therefore be implemented in a numerically stable way.

1 Introduction
2 Regularizability Conditions
3 A Reduced Form
4 Main Theorem
5 Conclusion
6 Appendix A

[1] A. Bunse-Gerstner, R. Byers, V. Mehrmann, and N. K. Nichols, “Feedback
design for regularizing descriptor systems”, Linear Algebra Appl., vol. 299,
pp. 119—151, 1999.
[2] A. Bunse-Gerstner, V. Mehrmann, and N. K. Nichols, “Regularization of descriptor
systems by derivative and proportional state feedback”, SIAM J. Matrix
Anal. Appl. Vol. 13, pp. 46—67, 1992.
[3] A. Bunse-Gerstner, V. Mehrmann, and N. K. Nichols, “Regularization of descriptor
systems by output feedback”, IEEE Trans. Automat. Control, AC-39,
pp. 1742—1747, 1994.
[4] D. J. Cobb, “Feedback and pole placement in descriptor variable systems”,
Internat. J. Control, vol. 33, pp. 1135—1146, 1981.
[5] F. R. Gantmacher, “Theory of Matrices”, vol. 2, Chelsea, New York, 1959.
[6] T. Geerts, “Solvability conditions, consistency, and weak consistency for linear
di®erential-algebraic equations and time-invariant linear systems: The general
case”, Linear Algebra Appl., vol 181, pp. 111—130, 1993.
[7] G. H. Golub and G. F. Van Loan, “Matrix Computations”, 2nd ed. Baltimore,
MD: Johns Hopkins Univ. Press, 1989.
[8] J. Kautsky, N. K. Nichols and E. K.-W. Chu, “Robust pole assignment in
singular control systems”, Linear Algebra Appl., vol. 121, pp. 9—37, 1989.
[9] F. Tisseur and K. Meerbergen, “The Quadratic Eigenvalue Problem”, SIAM
Review. Vol. 43, pp. 235—286, 2001.
[10] G. C. Verghese, B. C. L´evy, and T. Kailath, “A general state space for singular
systems”, IEEE Trans. Automat. Control, AC-26, pp. 811—831, 1981.
[11] E. L. Yip and R. F. Sincovec, “Solvability, controllability and observability of
continuous descriptor systems”, IEEE Trans. Automat. Control, AC-26, pp.
702—707, 1981.