  In this paper, some preliminaries about Morgan problem, signal flow graph and
controllable linear time-invariant standard system are first introduced in
detail. In order to synthesize the necessary and sufficient condition for
decoupling system, the first and second necessary conditions, and a sufficient
condition for decoupling a controllable linear time-invariant system are
secondly analyzed respectively. Therefore, the nonregular static state feedback
expression for decoupling system that ensures the internal stability of the
uncontrollable subsystem of the decoupled system at the same time is deduced.
Then the pole assignment for the controllable subsystem of a decoupled system
while ensuring its decoupled state is introduced. Finally, two examples
combined with their corresponding signal flow graphs show the simplicity and
feasibility of the necessary and sufficient condition for decoupling system
described in the paper.
