In this paper, the set stabilization problem of Markovian jump Boolean control networks (MJBCNs) is investigated via semi-tensor product of matrices. First, the conception of set stabilization is proposed for MJBCNs. Then based on the algebraic expression of MJBCN, a necessary and sufficient condition for set stabilization is provided by a linear programming problem, which is simple to solve. Moreover, by solving this linear programming problem, an algorithm for designing a state feedback controller is developed. Finally, two examples are presented to illustrate the feasibility of the obtained results.

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The Owen value is investigated in this paper. It is a generation of Shapley value as a solution of cooperative games with coalition structures. First, a characteristic function of a cooperative game is expressed as a pseudo‐logical function by using semi‐tensor product of matrices. Then, a matrix formula is given for calculating Owen values. The matrix formula not only makes computing more convenient but also facilitates theoretical analysis. Therefore, an application of Owen value in distributed welfare games is presented. Utility functions of a distributed welfare game with coalition structure are designed based on Owen value. Examples are showed to illustrate the theoretical results.

Fort Worth, TX 76118 Mechanical and Ampace Engineexkg University of Texas at Arlington Arlinaot~TX 76019 Moncrief-O'Donnell Chair for AutanaElectrical Engineering Department University of Texas at Arlington PkIington,TX 76019 Box 19023 Institute (ARRI) t ion and Robotics, ARRI 8 r7-794.5714Abstract A convergence theoxem is presented for an algorithm that solves an LQG conml problem which includes an pedormance bound. The mixed optimization problem setup results in a system of three Riccati equations, two of which are coupled and c8n not be solved independently. The algorithm rapidly converges to a global minimum under very general standard assumptions.