DocumentCode :
854403
Title :
The majorant Lyapunov equation: A nonnegative matrix equation for robust stability and performance of large scale systems
Author :
Hyland, David C. ; Bernstein, Dennis S.
Author_Institution :
Harris Corporation, Melbourne, FL, USA
Volume :
32
Issue :
11
fYear :
1987
fDate :
11/1/1987 12:00:00 AM
Firstpage :
1005
Lastpage :
1013
Abstract :
A new robust stability and performance analysis technique is developed. The approach involves replacing the state covariance by its block-norm matrix, i.e., the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics. A bound (i.e., majorant) for the block-norm matrix is given by the majorant Lyapunov equation, a Lyapunov-type nonnegative matrix equation. Existence, uniqueness, and computational tractability of solutions to the majorant Lyapunov equation are shown to be completely characterized in terms of M matrices. Two examples are considered. For a damped simple harmonic oscillator with uncertain but constant natural frequency, the majorant Lyapunov equation predicts unconditional stability. And, for a pair of nominally uncoupled oscillators with uncertain coupling, the majorant Lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators, a result not predictable from quadratic or vector Lyapunov functions.
Keywords :
Large-scale systems, linear; Lyapunov matrix equations; Robustness, linear systems; Covariance matrix; Equations; Frequency; Large-scale systems; Oscillators; Performance analysis; Robust stability; Robustness; Testing; Uncertainty;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1987.1104487
Filename :
1104487
Link To Document :
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