Abstract
In this paper, we study the guaranteed cost control for singularly perturbed systems with uncertainties. This is an extension of the work by Mukaidani et al. in the sense that the state and input matrices are allowed to be uncertain. A new method for decision of construction parameter in a controller is presented. We propose the ε-independent controller for the guaranteed cost control by solving the reduced-order algebraic Riccati equations and the Lyapunov equations only. Therefore, it is easy to construct the stabilizing controller for sufficient small because we need not solve the full-order algebraic Riccati equation or separate the slow and fast subsystems based on the existing method. On the other hand, when the parameter ε is not too small, we apply the exact decomposition technique to this problem. We newly show that the exact decomposition technique has property of quadratic convergence and that there exists a unique solution of the Riccati equation in the subset sufficiently close to the initial guess. A numerical example is given to show the potential of the proposed technique.
