Solution to Morgan Problem (2201.02908v4)

Abstract: 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.