The Lyapunov equation for n-dimensional discrete systems

The necessary and sufficient conditions for the existence of positive definite solutions to the n-D Lyapunov equation are presented. It is shown that there exist n-D stable systems for which no positive definite solutions to the n-D Lyapunov equation exist. Furthermore, it is pointed out that some results on the 2-D Lyapunov equation cannot be extended to either the three- or higher-dimensional case.<
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