The guaranteed cost control problem of uncertain singularly perturbed systems

In this paper we study the algebraic Riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system . The construction of the controller involves solving the full-order algebr aic Riccati equation with small parameter epsilon. Under control-oriented a ssumptions, we first provide the sufficient conditions such that the full-o rder algebraic Riccati equation has a positive semi-definite stabilizing so lution. Next we propose an iterative algorithm based on the Kleinman algori thm to solve the algebraic Riccati equation which depends on the parameter epsilon. Our new idea is to use the solutions of the reduced-order algebrai c Riccati equations fur the initial condition. By using the iterative algor ithm, we can easily obtain a required solution of the algebraic Riccati equ ation. Moreover, using the initial conditions without epsilon, we show that there exists an <(<epsilon>)over bar> such that the proposed algorithm has quadratic convergence. Finally, in order to show the effectiveness of the proposed algorithm, numerical examples are included. (C) 2000 Academic Pres s.