Stackelberg strategy for discrete-time stochastic system and its application to H2/H∞ control

In this paper, infinite-horizon Stackelberg strategy for discrete-time stochastic system is investigated. A necessary condition for the existence of the strategy set is derived by means of a set of cross-coupled stochastic algebraic Lyapunov and Riccati equations (CSALREs). In order to obtain a strategy set, Newton´s method is first considered. Second, a new algorithm based on semidefinite programming (SDP) is also given to avoid large computational dimension and complicated calculations for Jacobi matrix. The extension of results for H₂/H_∞ control problem based on Stackelberg strategy is also considered. Two numerical examples are exploited to show the usefulness of the strategies obtained.