The paper discusses the state equation of regular linear systems and in special conditions the solution of the state equation is obtained. the paper analyzes the Lyapunov stability of the regular linear systems. Through the in-deep research on Lyapunov theorem a new method to construct Lyapunov function is found. The solution of the Lyapunov equation is very important too. The author finds a way to solve the Lyapunov equation of the continuous or discrete regular linear systems. This approach suits to make a program to solve the Lyapunov equation on the computer.