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Bounded control and discrete-time controllability. (English) Zbl 0595.93008
Linear, finite-dimensional, time-invariant, discrete control systems are considered. Using the methods of convex analysis, necessary and sufficient conditions for complete controllability in finite time are formulated. It is assumed that the values of controls are taken from an arbitrary bounded and convex set, which does not necessarily contain the origin as a relative interior point. It is also noted that the class of systems that are bounded input controllable includes systems which are unstable. Partially, the paper extends the results given by B. Herz [”A contribution about controllability”, Advances in control systems and signal processing, Vol. 2, 275-298 (1981; Zbl 0499.93002)].
Reviewer: J.Klamka

##### MSC:
 93B05 Controllability 93B03 Attainable sets, reachability 93C55 Discrete-time control/observation systems 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces) 93C05 Linear systems in control theory 93C99 Model systems in control theory
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##### References:
 [1] DOI: 10.1016/0016-0032(61)90784-0 · Zbl 0161.15002 · doi:10.1016/0016-0032(61)90784-0 [2] DIEUDONNH J., Foundations of Modern Analysis (1969) [3] HERZ , B. , 1981 ,Advances in Control Systems and Signal Processing, Vol. 2 ( Weisbaden Friedr. Vieweg ), pp. 275 – 298 . [4] ROCKAFELLAR R. T., Convex Analysis (1970) · Zbl 0193.18401 [5] DOI: 10.1109/TAC.1963.1105535 · doi:10.1109/TAC.1963.1105535 [6] WONHAM W. M., Linear Multivariable Control a Geometric Approach (1979) · Zbl 0424.93001
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