Controllability and Reachability of Dynamic Discrete-Time Linear Systems

For discrete-time linear systems, controllability and reachability are not equivalent. Instead of the well-known Kalman's rank condition, which characterizes reachability, controllability to origin of the time invariant, discrete-time linear system is equivalent to the Fuhrmann's rank cond...

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Bibliographic Details
Main Authors: Molnar, S., Szigeti, F.
Format: Conference Proceeding
Language:English
Subjects:
Algebra
Continuous time systems
Control systems
Controllability
Discrete time systems
Kalman filters
Linear systems
Observability
Time varying systems
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Summary:For discrete-time linear systems, controllability and reachability are not equivalent. Instead of the well-known Kalman's rank condition, which characterizes reachability, controllability to origin of the time invariant, discrete-time linear system is equivalent to the Fuhrmann's rank condition. In the first part of this paper we prove that controllability to origin of time varying discrete-time linear systems, under a difference-algebraic condition, is equivalent to a generalized Fuhrmann's rank condition. In the second part we prove that reachability and observability for time varying discrete-time linear systems are equivalent to a structured Kalman's rank condition, under the difference algebraic independence of the structure matrices.
DOI:10.1109/ICCA.2003.1595043