W. Auzinger, A. Eder:
"A Note on Lyapunov transformation and exponential decay in linear ODE systems";
Mathematical Models & Methods in Applied Sciences, 11 (2001), 1; S. 23 - 31.

Kurzfassung englisch:
In this paper we consider a class of matrices A where all eigenvalues have negative real part and are of a common magnitude O(1). Concerning the behavior of e^{tA} we provide a necessary and sufficient condition, via Lyapunov transformation, for an estimate of the form ||e^{tA}\|_2 <= K_0 e^(-t/K_1) to be valid uniformly for t>0 with moderate-sized constants K_0 and K_1. All relevant relations are quantitatively specified.

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