Pole assignment by multirate sampled-data output feedback. (English) Zbl 0613.93040

Araki, Mituhiko; Hagiwara, Tomomichi

Int. J. Control 44, 1661-1673 (1986).

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

Keywords:

pole assignment; output feedback; multirate sampled-data control; time-invariant; continuous-time

References:

[1]	DOI: 10.1109/TAC.1986.1104205 · doi:10.1109/TAC.1986.1104205
[2]	ARAKI M., US-Japan Seminar on Recent Advances in Algebraic System Theory (1983)
[3]	DOI: 10.1109/TAC.1975.1101016 · doi:10.1109/TAC.1975.1101016
[4]	DOI: 10.1080/00207177808922419 · Zbl 0388.93021 · doi:10.1080/00207177808922419
[5]	COFFEY T. C., A.I.A.A. J. 4 pp 2178– (1966)
[6]	DOI: 10.1016/S0167-6911(82)80016-9 · Zbl 0489.93042 · doi:10.1016/S0167-6911(82)80016-9
[7]	DOI: 10.1080/00207178608933578 · Zbl 0592.93025 · doi:10.1080/00207178608933578
[8]	DOI: 10.1109/TAC.1967.1098564 · doi:10.1109/TAC.1967.1098564
[9]	KALMAN R. E., Proc. Conf. on Ordinary Differential Equations (1971)
[10]	DOI: 10.1016/0016-0032(59)90093-6 · Zbl 0142.07004 · doi:10.1016/0016-0032(59)90093-6
[11]	KALMAN R. E., Contrib. Diff. Eqns 1 pp 189– (1962)
[12]	DOI: 10.1109/TAC.1957.1104783 · doi:10.1109/TAC.1957.1104783
[13]	DOI: 10.1080/00207727908941606 · Zbl 0435.94017 · doi:10.1080/00207727908941606
[14]	DOI: 10.1109/TASSP.1976.1162760 · doi:10.1109/TASSP.1976.1162760