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Abstract: It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of x = Ax for some appropriate A. The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple numerical example is given. (Update)
Context of citations to this paper: More
.... uncertain linear systems [4] and conditions for existence of a common Lyapunov function which exploit positive realness [78, Chapter 33] [79], 80] We 15 believe that to make significant further progress, one must stay in close contact with particular applications that...
...hull of L matrices A1, AL C R X. For such systems, quadratic Lyapunov functions can be determined using convex programming techniques [1]. This paper de scribes an algorithm that either finds a quadratic Lyapunov function or terminates with a proof that no quadratic...
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BibTeX entry: (Update)
S. Boyd, and Q. Yang, "Structured and simultaneous Lyapunov functions for system stability problems," International Journal of Control, vol. 49, 2215--2240, 1989. http://citeseer.ist.psu.edu/boyd01structured.html More
@article{ boyd89structured,
author = "S. {BOYD} and Q. {YANG}",
title = "Structured and simultaneous {L}yapunov functions for system stability problems",
journal = "Int. J. Control",
volume = "49",
number = "6",
pages = "2215--2240",
year = "1989",
url = "citeseer.ist.psu.edu/boyd01structured.html" }
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