The recovery of sparse initial state based on compressed sensing for discrete-time linear system.

This paper considers the recovery of sparse initial state for deterministic discrete-time linear time-invariant systems based on the compressed sensing theory. A class of deterministic linear systems with the global observation matrices satisfying the restricted isometry property (RIP) is characterized. Sufficient conditions on the measurement time instants that guarantee the global observation matrix to be a RIP matrix are obtained. With respect to the recovery of the sparse initial state of a high-dimensional linear system, it is worth mentioning that the number of measurements can be significantly decreased in terms of compressed sensing theory. [ABSTRACT FROM AUTHOR]