engleski

On some properties of the Lyapunov equation for damped systems

We consider a damped linear vibrational system whose dampers depend linearly on the viscosity parameter $v$. We show that the trace of the corresponding Lyapunov solution can be represented as a rational function of $v$ whose poles are the eigenvalues of a certain skew symmetric matrix. This makes it possible to derive an asymptotic expansion of the solution in the neighborhood of zero (small damping).

Damped-vibration; Lyapunov equation; optimization of viscosities

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