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On the simultaneous diagonal stability of linear discrete-time systems

✍ Scribed by Tatsushi Ooba; Yasuyuki Funahashi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
98 KB
Volume
36
Category
Article
ISSN
0167-6911

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✦ Synopsis

This paper studies the set of time-invariant linear discrete-time systems in which each system has a diagonal quadratic Lyapunov function. First, it is shown that there is generally no common diagonal quadratic Lyapunov function for such a set of systems even if the set is assumed to be commutative. It is also shown that the commutativity assures the existence of a common diagonal quadratic Lyapunov function inside the set of 2 Γ— 2 systems or the set of nonnegative systems. Then, two simple topological results are presented concerning the simultaneous diagonal stability on the set of nonnegative systems. The ΓΏrst is a measure of the di erence of matrices that assures the simultaneous diagonal stability. The second is a measure of the commutativity of matrices.

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