skip to main content
article

Stability criteria for singular systems

Published: 01 June 2005 Publication History

Abstract

The different types of stability defined for the case of linear time invariant singular systems, namely systems modelled by differential and algebraic equations, are studied. In particular, new criteria are established for asymptotic stability, bounded input - bounded output (BIBO) stability, total and strong stability as well as the requirement of having free response being impulse free. For the derivation of the above results, the expansion of the resolvent matrix of the system in power series has been used.

References

[1]
1. Campbell, S. L. (1980). Singular systems of differential equations, New York: Pt. II, Pitman.
[2]
2. Cobb, J. D. (1984). Slow and fast stability in singular systems, Proc. 23rd Conf. Decision Contr., Las Vegas, NY, pp. 280-282.
[3]
3. Dai, L (1989). Singular Control Systems, Berlin: Springer-Verlag.
[4]
4. Doetsch, G. (1974). Introduction to the Theory and Application of the Laplace Transformation, Berlin: Springer-Verlag.
[5]
5. Kailath, T. (1980). Linear systems, New Jersey: Prentice-Hall.
[6]
6. Koumboulis, F. N. (1991). New Techniques for Analysis and Feedback Design for Regular and Singular Systems, Ph.D. Thesis, National Technical Univ. of Athens, Dept. of Electr. Eng.
[7]
7. Koumboulis, F. N. & Mertzios, B. G. (1998a). Stability criteria for singular systems, Proc. of the IFAC 1998 Symposium on Large Scale Systems: Theory and Applications (IFAC LSS '98), pp. 33-38, Rio, Patras, Greece, July 15-17 1998.
[8]
8. Koumboulis, F. N. & Mertzios, B. G. (1998b). P-D feddback for decoupling and pole assignment of singular systems, J. of Dynamic Systems, Measurement and Control, Transactions of ASME, v. 120, pp. 378-388.
[9]
9. Koumboulis, F. N. & Mertzios, B. G. (1999). On the Kalman's controllability and observability criteria for singular systems, Circuits, Systems and Signal Processing, v. 18, no. 3, pp. 269-290.
[10]
10. Koumboulis, F. N. & Paraskevopoulos, P. N. (1992). On the stability of generalized state space systems, IEEE Trans. on Circuits and Systems, v. 39, pp. 1006-1010.
[11]
11. Lewis, F. L. (1986). A survey of Linear Singular Systems, Circuits, Systems and Signal Processing, v. 5, pp. 3-36.
[12]
12. Lewis, F. L. & Mertzios, B. G. (1990). On the analysis of discrete linear time-invariant singular systems, IEEE Trans. Automat. Contr., v. 35, pp. 506-511.
[13]
13. Mertzios, B. G. & Lewis, F. L. (1989). Fundamental matrix of Discrete Singular Systems, Circuits, Systems and Signal Processing, v. 8, pp. 341-355.
[14]
14. Mertzios, B. G. (2000). Direct solution of continuous time singular systems based on the fundamental matrix, Proc. of the 8th IEEE Mediterrenean Conference on Control and Automation (MED 2000), Rio, Patras, Greece, 17-19 July 2000.

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Neural, Parallel & Scientific Computations
Neural, Parallel & Scientific Computations  Volume 13, Issue 2
June 2005
98 pages

Publisher

Dynamic Publishers, Inc.

United States

Publication History

Published: 01 June 2005

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 0
    Total Downloads
  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 25 Dec 2024

Other Metrics

Citations

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media