Method orderable cascade decomposition for control system

Abstract

In this paper, we propose a method to determine the state function and control function of the dynamical system represented by a system of equations with first-order partial derivatives under boundary and the first-order partial derivatives conditions of state function where are real matrices with corresponding sizes. The basis of the theory is a method to prove the orderable cascade decomposition to transform the original system into the equivalent system in the type . In the final step, we obtain the state function satisfying the conditions and substituting this in the previous step. Continuing this process, we can find out the state function and controllable function of the original dynamical system.