The Guaranteed Cost Control Problem of Uncertain Singularly Perturbed Systems

Abstract 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 algebraic Riccati equation with small parameter e. Under control-oriented assumptions, we first provide the sufficient conditions such that the full-order algebraic Riccati equation has a positive semi-definite stabilizing solution. Next we propose an iterative algorithm based on the Kleinman algorithm to solve the algebraic Riccati equation which depends on the parameter e. Our new idea is to use the solutions of the reduced-order algebraic Riccati equations for the initial condition. By using the iterative algorithm, we can easily obtain a required solution of the algebraic Riccati equation. Moreover, using the initial conditions without e, we show that there exists an e such that the proposed algorithm has quadratic convergence. Finally, in order to show the effectiveness of the proposed algorithm, numerical examples are included.

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