Glasnik Matematicki, Vol. 48, No. 2 (2013), 373-390.

OPTIMAL DAMPING OF THE INFINITE-DIMENSIONAL VIBRATIONAL SYSTEMS: COMMUTATIVE CASE

Ivica Nakić

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: nakic@math.hr


Abstract.   In this paper we treat the case of an abstract vibrational system of the form Mx″+Cx′+x=0, where the positive semi-definite selfadjoint operators M and C commute. We explicitly calculate the solution of the corresponding Lyapunov equation which enables us to obtain the set of optimal damping operators, thus extending already known results in the matrix case.

2010 Mathematics Subject Classification.   34G10, 70J99, 47D06.

Key words and phrases.   Vibrational systems, damping, Lyapunov equation.


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DOI: 10.3336/gm.48.2.10


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