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On the eigenvalue decay of solutions to operator Lyapunov equations (CROSBI ID 209600)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Grubišić, Luka ; Kressner, Daniel On the eigenvalue decay of solutions to operator Lyapunov equations // Systems & control letters, 73 (2014), 42-47. doi: 10.1016/j.sysconle.2014.09.006

Podaci o odgovornosti

Grubišić, Luka ; Kressner, Daniel

engleski

On the eigenvalue decay of solutions to operator Lyapunov equations

This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the k-th (generalized) eigenvalue decays exponentially in -sqrt(k), provided that the involved operator A generates an exponentially stable analytic semigroup, and A is either self-adjoint or diagonalizable with its eigenvalues contained in a strip around the real axis. Numerical experiments with discretizations of 1D and 2D PDE control problems confirm this decay.

Balanced truncation ; Exponential decay ; Lyapunov equation

Rad je sufinanciran i po Sveučilištu u Zagrebu, projekti br. 4.1.2.3. i K2.101.

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Podaci o izdanju

73

2014.

42-47

objavljeno

0167-6911

1872-7956

10.1016/j.sysconle.2014.09.006

Povezanost rada

Matematika

Poveznice
Indeksiranost