Existence and uniqueness conditions for the periodic solutions of the discrete-time periodic Lyapunov equation

1 December 1986

conference paper
Published by Institute of Electrical and Electronics Engineers (IEEE)

Vol. 25, 1439-1443
https://doi.org/10.1109/cdc.1986.267108

Abstract

In this paper, the discrete-time periodic Lyapunov equation (DPLE) is considered. Criteria for the existence and the uniqueness of periodic solutions of DPLE are worked out. It is also treated the case of positive (semi)definite solutions. To this aim, reference is made to the controllableuncontrollable decomposition of the periodic pair underlying DPLE.

Keywords

EQUATIONS
MATRIX DECOMPOSITION
EIGENVALUES AND EIGENFUNCTIONS
SUFFICIENT CONDITIONS
KALMAN FILTERS
CONTROL SYSTEMS
CONTROLLABILITY
SYMMETRIC MATRICES
ARTIFICIAL INTELLIGENCE
NOISE MEASUREMENT

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