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 kth (generalized) eigenvalue decays exponentially in root 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. (C) 2014 Elsevier B.V. All rights reserved.


Published in:
Systems & Control Letters, 73, 42-47
Year:
2014
Publisher:
Amsterdam, Elsevier Science Bv
ISSN:
0167-6911
Keywords:
Laboratories:




 Record created 2014-12-30, last modified 2018-03-17


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