Robust finite-time [formula omitted] control for Itô stochastic semi-Markovian jump systems with delays.

• There are few attempts to research semi-Markovian jump systems subject to generally uncertain TRs, Wiener process, state delays as well as input constraint at present. • For the semi-Markovian jump systems subject to generally uncertain TRs as well as Wiener process, the dynamic output feedback controller is proposed, which is studied rarely at present, and the state values are no longer required. • For the semi-Markovian jump systems subject to generally uncertain TRs as well as Wiener process, the FTB issue is little studied. This paper concentrates on robust finite-time H ∞ control for uncertain Itô stochastic semi-Markovian jump systems with generally uncertain transition rates, multiple state delays and input constraint. There are few attempts for Itô stochastic semi-Markovian jump systems with generally uncertain transition rates. In contrast to the existing results, the system explored in this paper is more general and has more potential applications. By means of the partial transition rate information, a semi-Markovian jump controller is developed to realize fault-tolerant control. Then, a closed-loop system can be gathered. Moreover, a cluster of stability conditions are attained via stochastic Lyapunov function with the way of linear matrix inequalities. Finally, two examples are presented to illustrate this effectiveness of the approach depicted in the work. [ABSTRACT FROM AUTHOR]