LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Halikias, G.; Karcanias, N.; Papageorgiou, A. (2013)
Publisher: Elsevier
Languages: English
Types: Article
Subjects: QA
The notion of “strong stability” has been introduced in a recent paper [12]. This notion is relevant for state-space models described by physical variables and prohibits overshooting trajectories in the state-space transient response for arbitrary initial conditions. Thus, “strong stability” is a stronger notion compared to alternative definitions (e.g. stability in the sense of Lyapunov or asymptotic stability). This paper defines two distance measures to strong stability under absolute (additive) and relative (multiplicative) matrix perturbations, formulated in terms of the spectral and the Frobenius norm. Both symmetric and non-symmetric perturbations are considered. Closed-form or algorithmic solutions to these distance problems are derived and interesting connections are established with various areas in matrix theory, such as the field of values of a matrix, the cone of positive semi-definite matrices and the Lyapunov cone of Hurwitz matrices. The results of the paper are illustrated by numerous computational examples.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [G] Golub W., Elementary diviors and some properties of the Lyapunov mapping, Rep. ANL-6465, Argonne National Laboratory, Argonne, IL, 1961.
    • [H] D. Hershkowitz, On cones and stability, Linear Algebra and its Applications, pp. 249-259, 1998.
    • [HP] D. Hinrichsen and A.J. Pritchard, Mathematical Systems Theory I, Texts in Applied Mathematics Vol. 41, Springer-Verlag, New York, 2005.
    • [HP2] D. Hinrichsen and A.J. Pritchard, On the transient behaviour of stable linear systems. Proc. 14th Int. Symp. Math. Theory Networks and Systems, Perpignan, France, 2000.
    • [S2] M.N. Spijker, Numerical ranges and stability estimates, Applied Numerical Mathematics, 13, pp. 241-249, 1993.
    • [SW] C. Scherer and S. Weiland, Lecture Notes DISC Course on Linear Matrix Inequalities in Control, Version 2, April 1999.
    • [SIG] R. E. Skelton, T. Iwasaki, and K. Grigoriadis, A uni ed approach to linear control design, Taylor and Francis series in Systems and Control, Bristol-USA, 1997.
    • [W] J.E. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, 1965.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article