Abstract: 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.

Key words: Semi?Markov jump linear system (S?MJLS), Reachable set, Mismatched mode, Linear matrix inequalities (LMIs)

摘要： 研究了控制器模态不匹配的半马尔可夫跳变线性系统的可达集。在不考虑有界转移速率约束的情况下，设计了模态与系统模态不匹配的控制器，得到了系统状态轨迹有界的充分条件。然后，分别研究了模态独立和模态依赖的控制策略，进一步讨论矩阵中含有不确定的概率和部分已知的矩阵情况。最后，通过算例和仿真结果验证了模态不匹配控制方法的有效性和优越性。

关键词: 半马尔可夫跳变线性系统, 可达集, 模态不匹配, 线性矩阵不等式