Method orderable cascade decomposition for control system

Tóm tắt

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.