Observer-based integral sliding mode control for uncertain neutral semi-Markovian jumping systems with time-varying delays

This article studies the observer-based integral sliding mode control (ISMC) problem for continuously uncertain neutral semi-Markovian jumping systems with time-varying delays (TDs). Firstly, based on the designed state observer, an ISMC method is proposed for the first time. Then, building an appropriate stochastic Lyapunov-Krasovskii functional by taking into account more information about TDs, a novel sufficient condition is established for the robustly stochastic stability of the overall system made up of the error system and the sliding mode dynamics system. Furthermore, an ISMC law is devised to ensure the reachability of the integral sliding surface in a finite time. Additionally, the proposed method can be reduced to the known state case, thus, the ISMC problem for continuously uncertain neutral semi-Markovian jumping systems with TDs is also investigated in this article. Finally, three numerical examples explain the effectiveness of the results obtained.