Some invariants of discrete-time descriptor systems

Many papers analyze the role of controllability and observability indices of normal linear systems in control theory and their use in the study of structural properties. This work introduces these indices for linear discrete-time descriptor systems. Such indices are studied in two different ways, by means of the state-space approach and using its transfer matrix . A canonical form of the state-space system and a special decomposition of the nonproper transfer matrix are considered in order to discuss the reachability and observability indices.

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