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

@article{Bolzern1986ExistenceAU,
  title={Existence and uniqueness conditions for the periodic solutions of the discrete-time periodic Lyapunov equation},
  author={Paolo Bolzern and Patrizio Colaneri},
  journal={1986 25th IEEE Conference on Decision and Control},
  year={1986},
  pages={1439-1443}
}
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. 
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