An Accurate and Fast Algorithm for the Lyapunov Matrix Differential Equation Arising From Input–Output Finite-Time Stability of Linear Systems

Abstract

The Lyapunov matrix differential equation (LDE) is of great significance in modern control theory and practical engineering applications. In this study, we propose a novel algorithm based on matrix series to solve the LDE, which fully utilizes the properties of matrix series and matrix powers. Rigorous convergence and error analyses illustrate its reliability. Furthermore, we establish that the error norm between the exact LDE solution and the numerical solution using our proposed algorithm can be less than a preset error precision. Finally, several numerical experiments demonstrate the effectiveness of the algorithm and its superior performance compared to existing classical methods. This advance enables faster and more reliable input–output finite-time stability assessments for linear systems.