Conditions for the non-negativity of integral quadratic forms with constant coefficients on a half-axis

A. A. Milyutin

N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences

Abstract: An integral quadratic functional with constant coefficients on a half-axis is considered. A necessary and sufficient condition for its non-negativity at all square integrable pairs of functions related by a linear ODE is proposed, which is based on the Hamilton–Jacobi inequality. A connection between this condition and the well-known frequency criterion is established.

UDC: 517.97

MSC: Primary 49N10; Secondary 49L99

Received: 19.09.2001

DOI: 10.4213/sm644

 English version: Sbornik: Mathematics, 2002, 193:4, 531–557

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