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

The guaranteed cost control (GCC) problem for uncertain stochastic systems with NN 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.