research article text
oaioai:hrcak.srce.hr:112214

Optimal damping of the infinite-dimensional vibrational systems: commutative case

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Publication date
1 January 2013
Publisher
Department of Mathematics, University of Zagreb
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    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

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