Controllability of Multiple Input Discrete-Time Linear Systems with Positive Controls

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  • Controllability of Multiple Input Discr

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The controllability with input constraints is important in practical problems. Especially, the controllability with positive controls is useful in discussing the vibration control problem of a pendulum system, economic system, etc. And so, this paper presents a necessary and sufficient condition for the controllability to the zero state by positive controls of multiple input discrete-time linear systems. It is derived that the positive controllability of a given system may be reduced to those of its subsystems corresponding to the the Jordan canonical form. Since the sizes of the subsystems are smaller than that of a given system, then the positive controllability test can be simplified very much. Furthermore, the structure of a positive controllable system is revealed. The results in this paper are fundamental and essensial in the control system theory.

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