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Generalized matrix diagonal stability and linear dynamical systems

โœ Scribed by Octavian Pastravanu; Mihail Voicu

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
176 KB
Volume
419
Category
Article
ISSN
0024-3795

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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.

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Tangent spaces in non-linear dynamical systems are state dependent. Hence, it is generally not possible to exactly represent a non-linear dynamical system by a linear one over "nite segments of the evolving trajectories in the phase space. It is known from the well-known theorem of Hartman and Grobm