Solving Lyapunov equations symbolically

Symbolic manipulation is an indispensable tool in control design and in system analysis. While numeric computational languages and algorithms have been exhaustively used, symbolic manipulation methods have been barely used at all. In this study, we developed a Maple language procedure to solve continuous Lapunov equations symbolically in conjunction with the Kronecker product. A Lyapunov continuous algebraic equation of the form A/sup T/P+PA+Q=0 was considered. The method is also applicable to time-variant and non-constant systems. Examples were incorporated to test the method over different order systems and results were compared with the published solutions of Gonzalez and Munro (1990, 1991). A thorough study of the system stability of a non-constant system matrix A is also introduced and analyzed. Maple source code procedures are presented and fully commented on.