Titlebook: Control Problems of Discrete-Time Dynamical Systems; Yasumichi Hasegawa Book 2013 Springer-Verlag Berlin Heidelberg 2013 Control Problems.

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Introduction,also known that the output value of a state may be different from the output value of the preceding state. If we want to construct a control system to be smooth and gradual, we may consider input output control problems. Therefore, in the sense of input and output, control problems of input output a

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Control Problems of Affine Dynamical System,p with causality. Affine dynamical systems were proposed and the realization problem of the systems was solved in the reference [Matsuo & Hasegawa, 2003].We characterized the finite dimensionality of affine dynamical systems. We obtained the same results as ones established in linear system theory.

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Control Problems of Linear Representation Systems, for any causal input/output map, i.e., any input response map, there exist at least two canonical, namely quasi-reachable and distinguishable linear representation systems which realize, equivalently, faithfully describe it, and any two canonical linear representation systems with the same behavior

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Variational Methods in Theoretical Mechanics be smooth and gradual, we may consider input output control problems. Therefore, in the sense of input and output, control problems of input output are more practical than control problem of input and state which is used in the usual control problem.

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