Output dead-beat controllers and function dead-beat observers for linear periodic discrete-time systems†

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Abstract
In this paper two problems are considered: that of finding a (possibly dynamic) linear periodic controller such that both the regulated output and the control input of a linear periodic discrete-time system become and remain zero, and that of designing a dead-beat observer of a linear function of the state of the system. For both these problems necessary and sufficient conditions for the existence of a solution are given, and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs. Such conditions are very simple and concise when expressed in terms of controllable and/or unreconstructible states.

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