  In this article, the definition on the control ability, and the relation
between the open-loop control ability and the closed-loop performance are
studied systematically for the linear dynamical systems. Firstly, to define and
compare rationally the state control ability between the different controlled
plants or one controlled plant with the different system parameters, the
normalization of the input variables, the state variables, the system mdeols
are discussed. With the help of the normalization, the state control ability
with the time attribute can be difined under the unit input constraint (input
amplitude limited). And then, two theorems on the relations among the open-loop
control ability, the control strategy space (i.e., the solution space of the
input variables for control problems), and the closed-loop performance with the
time attribute are purposed and proven. Based on that, the conclusion that it
is very necessary to optimize the control ability for the practical engineering
problems can be got. Finally, the simulation experiments show us the
normalizing the variables and system models, and comparing the contol ability
between the different controlled palnts.
