Technical Notes and Correspondence: The Recursive Reduced-Order Numerical Solution of the Singularly Perturbed Matrix Differential Riccati Equation

Under stabilizability-observability conditions imposed on a singularly perturbed system, an efficient numerical method for solving the corresponding matrix differential Riccati equation is obtained in terms of the reduced-order problems. The order reduction is achieved via the use of the Chang transformation applied to the Hamiltonian matrix of a singularly perturbed linear-quadratic control problem. In addition, an efficient numerical recursive algorithm with the quadratic rate of convergence is developed for solving algebraic equations comprising the Chang transformation.