Abstract
Let b k (t) (t≥ 0; k=1, ... , n) be real non-negative scalar-valued functions having continuous derivatives up to n–k-th order. Consider the gradient-type equation
\(\displaystyle P(D)x(t) = \sum_{k=0}^{n-1}\frac{d^k}{dt^k}(b_{n-k} (t)x(t))\quad (t\geq 0), \quad\quad (1.1) \)
where
\(\displaystyle D \equiv \frac{d}{dt}; P(\lambda) = \lambda^n + c_1 \lambda^{n-1} + \ldots + c_n (c_k \equiv const > 0)\quad\quad(1.2) \)
is a Hurwitzian polynomial.
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Gil’, M.I. 10. Aizerman’s Problem for Nonautonomous Systems. In: Explicit Stability Conditions for Continuous Systems. Lecture Notes in Control and Information Science, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11311959_11
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DOI: https://doi.org/10.1007/11311959_11
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