The reachable set analysis for the semi⁃Markov jump linear system (S⁃MJLS) with mismatched control form was researched. Without considering the bounded transfer rate constraint,a controller was designed that allowed the controller mode to be mismatched with the system mode, sufficient conditions were gotten that the system state trajectory was bounded. Then, control strategies of mode independent and mode dependent were also considered, some generalizations of uncertain and partially known correlation matrices were further discussed.Finally, the effectiveness and superiority of modal mismatch control methodwere verified by examples and simulation results.

This paper focused on the consensus problem of linear multi⁃agent systems via a pinning controller with protocol failure. A network model of connection failure was established,the dwell time of the model was constant.A Lyapunov function approach based on such two states was developed to analyse its consensus. Concise conditions with smaller computation complexity were proposed and depended on such dwell times. Then, two sufficient conditions for the existence of a pinning consensus controller with failures were established. Finally, a practical example was used to demonstrate the effectiveness of the proposed methods.