The Cross Gramian is a mathematical construct used in the fields of control theory, signal processing, and systems theory. It is primarily associated with the analysis of linear time-invariant (LTI) systems and helps in understanding the relationships between different input-output systems. Given two linear systems described by their state-space representations, the Cross Gramian can be used to quantify the interaction between these systems. Specifically, it can be applied to determine controllability and observability properties when dealing with multiple systems.
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