Finite Horizon Optimal Control of Singularly Perturbed Systems: A Differential Lyapunov Equation Approach $ $

In this note, we study the finite time (horizon) optimal control problem for singularly perturbed systems. The solution is obtained in terms of the corresponding solution of the algebraic Riccati equation and the decomposition of the singularly perturbed differential Lyapunov equation into reduced-order differential Lyapunov/Sylvester equations. An illustrative numerical example is provided to show the efficiency of the proposed approach.