Robust guaranteed cost control for uncertain stochastic systems with multiple decision makers

The guaranteed cost control (GCC) problem for uncertain stochastic systems with N decision makers is investigated. It is noteworthy that the necessary conditions, which are determined from Karush-Kuhn-Tucker (KKT) conditions, for the existence of a guaranteed cost controller have been derived on the basis of the solutions of cross-coupled stochastic algebraic Riccati equations (CSAREs). It is shown that if CSAREs have an optimal solution, then the closed-loop system is exponentially mean square stable (EMSS) and has a cost bound. In order to simplify computations and attain a global optimum, the linear matrix inequality (LMI) technique is also considered. Finally, a numerical example for a practical megawatt-frequency control problem shows that the proposed methods can help in attaining an adequate cost bound. Furthermore, the features of these methods are characterized.