A robust static output feedback(SOF)Stackelberg game with multiple followers in stochastic linear parameter varying(LPV)systems is investigated.The conditions for the existence of a robust SOF Stackelberg strategy set under H∞ constraints are established by the cross-coupled matrix inequality(CCMI).To determine this strategy set,the optimization problems corresponding to the relevant cost bounds are defined,and their solution sets are derived using the Karush-Kuhn-Tucker conditions.The results show that the robust SOF Stackelberg strategy set can be obtained by solving higher-order cross-coupled matrix equations(CCMEs).Because CCMEs are complex and difficult to solve numerically,a heuristic algorithm is developed by combining the CCMEs with the CCMIs.The convergence property is proven using the Krasnoselskii-Mann(KM)iteration algorithm.Finally,two numerical examples are solved to demonstrate the reliability and usefulness of the proposed heuristic algorithm.