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Pole assignment by multirate sampled-data output feedback. (English) Zbl 0613.93040
This paper considers multirate sampled-data control of a linear time- invariant continuous-time system. It is shown that, if the system is controllable and observable, a multirate sampled-data ’gain’ controller can always be constructed and the poles of the closed-loop system can be assigned an arbitrary given symmetric set of complex numbers. Moreover, ’locally minimum controllability indices LMCI’ are defined as a set of integers $$(n_ 1,...,n_ m)$$ such that $$\sum^{m}_{i=1}n_ i$$ equals the dimension of the state vector and the matrix $$[b_ 1,...,A^{n_ 1-1}b_ 1,...,b_ m,...,A^{n_ m-1}b_ m]$$ is non- singular. It is obvious that the Kronecker invariants are LMCI. It is shown that the input sampling rate $$(N_ 1,...,N_ m)$$ can be chosen equal to LMCI. This method has the following properties:
(1) Sampling of the output is done less often than sampling of the input.
(2) Only a gain controller is used.
(3) The designed controller becomes stable.
These properties do not always imply the advantages of this method, but, at least, suggest a new perspective.
Reviewer: M.Kono

##### MSC:
 93C57 Sampled-data control/observation systems 93B55 Pole and zero placement problems 93C05 Linear systems in control theory 93B25 Algebraic methods 93B05 Controllability
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