Based on the interval type-2 fuzzy (IT2F) approach, this article investigates the fault detection filter design problem for a class of nonhomogeneous higher level Markov jump systems with uncertain transition probabilities. Considering that the mode information of the system cannot be obtained synchronously by the filter, the hidden Markov model can be seen as a detector to handle this asynchronous problem, and the parameter uncertainty can be processed by the IT2F approach with the lower and upper membership functions. Then, the asynchronous IT2F filter is designed to deal with the fault detection problem. Furthermore, the Gaussian transition probability density function is introduced to describe the uncertainty transition probabilities of the system and the filter. Based on the Lyapunov theory, the existence of the designed asynchronous IT2F filter and the dissipativity of the filter error system can be well ensured. In this article, the simulation study on a quarter-car suspension system verifies that the designed asynchronous IT2F filter can detect faults without error alarms.

This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given L₂ performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka-Volterra population model is used to show the feasibility and validity of the main results.

This article addresses the design issue of fuzzy asynchronous fault detection filter (FAFDF) for a class of nonlinear Markov jump systems by an event-triggered (ET) scheme. The ET scheme can be applied to cut down the transmission times from the system to FAFDF. It is assumed that the system modes cannot be obtained synchronously by the filter, and instead, there is a detector that can measure the estimated modes of the system. The asynchronous phenomenon between the system and the filter is characterized via a hidden Markov model with partly accessible mode detection probabilities. Applying the Lyapunov function methods, sufficient conditions for the presence of FAFDF are obtained. Finally, an application of a wheeled mobile manipulator with hybrid joints is employed to clarify that the devised FAFDF can detect the faults without any incorrect alarm.

In this article, the problem of the asynchronous fault detection (FD) observer design is discussed for 2-D Markov jump systems (MJSs) expressed by a Roesser model. In general, the FD observer cannot work synchronously with the system, that is, the mode of the observer varies with the mode of the system in line with some conditional transitional probabilities. For dealing with this difficult point, a hidden Markov model (HMM) is employed. Then, combining the $H_{\infty }$ attenuation index and $H_{\_{}}$ increscent index, a multiobjective solution to the FD problem is formed. In terms of linear matrix inequality technology, sufficient conditions are gained to guarantee the existence of the asynchronous FD. Simultaneously, an asynchronous FD algorithm is generated to acquire the optimal performance indices. Finally, a numerical example concerned with the Darboux equation is demonstrated to exhibit the soundness of the developed approach.

This article focuses on the finite-time asynchronous output feedback control scheme for a class of Markov jump systems subject to external disturbances and nonlinearities. The conic-type nonlinearities hold a constraint condition which locates in a known hyper-sphere with an indefinite center. In addition, the asynchronization phenomenon occurs between the system and the controller, which can be represented by means of a hidden Markov model. A sufficient condition is derived not only to guarantee the finite-time boundedness of the acquired closed-loop systems but also to possess a desired $H_{\infty }$ performance on the basis of Lyapunov functional technique. Finally, the validity and feasibility of the proposed method are demonstrated with a dc-motor experiment.