Finite‐time fault detection for multiple delayed semi‐Markovian jump random systems

Abstract

This work focuses on the problem of finite‐time multiple delay‐dependent filter‐based fault detection (FD) and fault‐tolerant control (FTC) for semi‐Markovian jump random nonlinear systems subject to state and input constraints. There are model uncertainties, multiple time‐varying delays, nonlinear dynamics as well as faults in these systems. This study is the first time to try. In addition, this article both considers stochastic finite‐time boundedness and input–output finite‐time mean square stabilization. A semi‐Markovian jump filter, a semi‐Markovian jump controller and a fault weighting system are developed to achieve FD and FTC. Then, an augmented closed‐loop nonlinear system can be established. Moreover, multiple delay‐dependent sufficient conditions are produced by means of stochastic Lyapunov function in this framework of linear matrix inequalities. Finally, an example is shown to bring out the effectiveness of the method addressed in this study.

Finite‐time fault detection for nonlinear delayed system with dynamic quantization and multiple packet dropouts

“…In the work of Luo et al, 39 the problem of simultaneous finite‐time FD and control for singular Markovian jump system has been investigated, where the FD filter and controller have been designed and conclusions on the stochastic finite‐time stability of augmented system have been drawn by choosing appropriate Lyapunov functions. Moreover, similar problem has been investigated for semi‐Markovian jump system in the work of Sun et al, 40 where both the input‐output finite‐time mean square stabilization and stochastic finite‐time boundedness of the FD system have been considered. However, it is worth noting that the current study on finite‐time FD problem is not adequate, which constitutes another research motivation of this article.…”

Dissipative fault detection for time‐delay nonlinear Markov jump systems with measurement outliers under stochastic communication protocol

“…[11][12][13][14] Accordingly, a lot of studies about fault detection (FD) problems for time-delay MJSs with different characteristics have been developed. [15][16][17][18] To mention a few, the FD filter has been designed for time-delay MJSs with partially available modes in Reference 17, in which the signals emitted from detector have been utilized when the information of system modes is missing. Moreover, the adaptive event-triggered FD problem has been investigated for asynchronous T-S fuzzy networked MJSs with time-varying delays in Reference 18, where sufficient conditions have been obtained to guarantee that the error augmented system is stochastically stable.…”

“…On the other hand, fault is a serious threat to the system safety, which may cause huge losses if it occurs but cannot be detected in time 11‐14 . Accordingly, a lot of studies about fault detection (FD) problems for time‐delay MJSs with different characteristics have been developed 15‐18 . To mention a few, the FD filter has been designed for time‐delay MJSs with partially available modes in Reference 17, in which the signals emitted from detector have been utilized when the information of system modes is missing.…”

Adaptive sliding mode control for semi‐Markov jump uncertain discrete‐time singular systems

“…Naturally, the semi-Markov process that allows the ST to obey an arbitrary probability distribution in any mode and still satisfies the Markov hypothesis more flexibly has attracted interest. [8][9][10][11][12][13] The semi-Markov process has gained attention in continuous-time SS, please see References 14, 15, and the references therein. In contrast, there is still more space for DT singular semi-Markov jump systems (SSMJSs).…”

“…But this hypothesis is restrictive on the distribution of sojourn‐time (ST) in each mode, that is, the ST obeys geometric and exponential distributions in the discrete and continuous situations, respectively, which is a big drawback of applying the Markov process. Naturally, the semi‐Markov process that allows the ST to obey an arbitrary probability distribution in any mode and still satisfies the Markov hypothesis more flexibly has attracted interest 8‐13 . The semi‐Markov process has gained attention in continuous‐time SS, please see References 14, 15, and the references therein.…”