Finite-time sliding-mode control for semi-Markov systems with delayed impulses

Dear Editor, This letter concerns the design of sliding mode control (SMC) for semi-Markov switching systems with time-varying transmission and impulse delay. The difficulties of this problem are: 1) Time-varying transmission and impulse delay bring more nonlinear dynamic characteristics and lag effects; 2) Semi-Markov mode switching introduces uncertainty; 3) The reachable stage and sliding stage are affected by two types of impulses in the system, which increases the complexity of theoretical derivation.