H∞ control for networked semi-Markovian jump systems with generally incomplete transition probabilities and distributed delays

The $H_{\infty }$ control problem for networked semi-Markovian jump systems (S-MJSs) with generally incomplete time-varying transition probabilities (GITTPs) and distributed delays is addressed in this article. Firstly, the TPs considered herein may be exactly known, merely known with lower and upper bounds, or unknown, meanwhile the distributed delays own a probability density function as its kernel. Secondly, the closed-loop networked S-MJSs is established with GITTPSs and distributed delays. Thirdly, to make full use of the characteristic of delay probability distribution, a generalized discrete-Bessel summation inequality and a Lyapunov–Krasovskii functional (LKF) are developed by distributed kernel. Then, by applying the Lyapunov method with generalized summation inequality and utilizing an equivalent transformation method to deal with the unknown TPs, several sufficient conditions that guarantee a prescribed $H_{\infty }$ performance for networked S-MJSs are established. Eventually, two simulation examples including a single machine infinite bus power systems are presented to illustrate the effectiveness of the proposed theoretical findings.