Guaranteed cost control for uncertain stochastic multimodeling systems

The guaranteed cost control problem for stochastic multimodeling systems with norm bounded uncertainty is investigated. The main contribution in this paper is that a new parameter independent controller is derived by solving the reduced-order slow and fast stochastic algebraic Riccati equations (SAREs) whose dimension is smaller than the dimension of full-order stochastic multimodeling algebraic Riccati equation (SMARE). It is shown that if these AREs have positive definite stabilizing solution then the closed-loop system is quadratically stable and has the cost bound. A numerical example for a practical megawatt-frequency control problem will be solved to show the effectiveness of the proposed optimization algorithm.