Closed-Form Solutions to Continuous-Time Algebraic Riccati Equation for Second-Order Systems

Abstract

Two closed-form methods to solve the continuous-time algebraic Riccati equation (CARE) for second-order systems in terms of the mass, damping, and stiffness matrices are presented. One method utilizes the modal transformation of mass and stiffness matrices, and the other does not require this transformation. Hundreds of high-dimensional second-order systems are used to show that these methods achieve similar or better accuracy compared to the state-of-the-art, while significantly reducing the computation time. Furthermore, advantages of these methods are illustrated in vibration control problems.