This paper examines the adaptive event-triggered fault detection problem of semi-Markovian jump systems (S-MJSs) with output quantization. First, we develop an adaptive event-triggered scheme for S-MJSs that is more effective than conventional event-triggered strategy for decreasing network transmission information. Meanwhile, we design a new adaptive law that can dynamically adjust the event-triggered threshold. Second, we consider output signal quantization and transmission delay in the proposed fault detection scheme. Moreover, we establish novel sufficient conditions for the stochastic stability in the proposed fault detection scheme with an H∞ performance with the help of linear matrix inequalities (LMIs). Finally, we provide simulation results to demonstrate the usefulness of the developed theoretical results.

This paper studies the fault detection problem for continuous-time fuzzy semi-Markov jump systems (FSMJSs) by employing an interval type-2 (IT2) fuzzy approach. Firstly, the continuous-time FSMJSs model is designed and the parameter uncertainty is addressed by the IT2 fuzzy approach, where the characteristic of sensor saturation is taken into account in the control system. Secondly, the IT2 fuzzy semi-Markov modedependent filter is constructed, which is employed to deal with the fault detection problem. Then, by using Lyapunov theory, it can be guaranteed that the constructed fault detection model based on this filter and IT2 FSMJSs is stochastically stable with H1 performance. Moreover, the quantization strategy is applied to the fault detection plant to dispose of the problem of limited network bandwidth. Compared with the existing literature, the differences mainly lie in two aspects, one is that the IT2 fuzzy method is utilized for FSMJSs to tackle the parameter uncertainty of system, and the other is to detect the fault signal of IT2 FSMJSs by using the fault detection system which is constructed based on the IT2 fuzzy semi-Markov mode-dependent filter and IT2 FSMJSs. Finally, two simulation examples are provided to illustrate the effectiveness and the usefulness of the proposed theoretical method.

This article focuses on the finite-time guaranteed cost (FTGC) control problem for interval type-2 (IT2) fuzzy semi-Markov switching systems (S-MSSs) with additive disturbances. Based on the IT2 fuzzy S-MSSs and the state feedback control method, a novel IT2 mode-dependent fuzzy guaranteed cost (GC) controller is developed under the mismatched membership functions. Then, some new sufficient conditions are given to ensure that IT2 fuzzy S-MSSs are finite-time (FT) stochastically stable based on the designed IT2 mode-dependent fuzzy GC controller. Furthermore, the transition rate boundary condition is relaxed, and a new incomplete transition rate boundary model is constructed to reflect the transition rate information. For both the incomplete transition rate boundaries and the actuator fault phenomenon, the improved stability criteria are provided to stabilize the IT2 fuzzy S-MSSs within an FT interval and determine the gains of the IT2 mode-dependent fuzzy GC controller, resulting in a much greater design flexibility. Distinct from the existing results, the presented FTGC control scheme is more suitable for many practical systems because the IT2 fuzzy S-MSS model, which is more general compared with the traditional fuzzy system and S-MSSs, is considered. Finally, three illustrative examples are offered to explain the effectiveness and feasibility of the proposed FTGC control approach.

This article deals with the fault detection problem for a class of Takagi–Sugeno (T–S) fuzzy semi-Markov jump systems (FSMJSs) with partly unknown transition rates (PUTRs) subject to output quantization by designing a reduced-order filter. First, a more general PUTRs model is constructed to describe the situation that the information of some elements is completely unknown, where this model is affected simultaneously by PU information and time-varying parameter compared with the traditional PUTRs model. Second, we take full advantage of the reduced-order filter to address the fault detection problem for FSMJSs, in which the stochastic failure phenomenon is injected into the reduced-order filter. Besides, the logarithmic quantizer is employed to tackle the limited bandwidth problem in a communication channel. Consequently, the new sufficient conditions are developed based on the Lyapunov theory to obtain the desired reduced-order filter. Simulation results with respect to the tunnel diode circuit are provided to demonstrate the usefulness and availability of the established theoretical results.