In this paper, the finite-time memory fault detection filter (MFDF) is designed for nonlinear discrete systems with randomly occurring deception attacks, where the phenomenon of the randomly occurring deception attacks is characterised by a Bernoulli distributed random variable with known probability. To be specific, the finite-horizon data are employed to construct the MFDF. The main purpose of this paper is to design the MFDF such that, for all nonlinearities, external disturbances and randomly occurring deception attacks, the resultant augmented system is finite-time stable and attains the $H_{\mathrm{\infty }}$ performance. Accordingly, some sufficient conditions are developed to guarantee the existence of the desired fault detection filter parameters, where the solvability of the addressed problem is verified by the feasibility of certain matrix inequalities. Moreover, in order to show that the MFDF has better detection performance, a non-memory fault detection filter (NMFDF) is constructed to compare with the MFDF. Finally, two numerical simulations are utilised to illustrate the effectiveness of the proposed fault detection strategies and explain the superiority of the proposed MFDF.

This paper is concerned with the problem of robust adaptive sliding mode control (RASMC) for discrete singular systems subject to randomly occurring mixed time-delays (ROMTDs) under uncertain occurrence probabilities. The mixed time delays are considered, which are comprised of both the discrete interval delays and infinite distributed delays. Meantime, two random variables obeying the Bernoulli distribution are utilised to depict the phenomena of randomly occurring discrete time-varying delay and distributed time-delay, in which the uncertain occurrence probabilities are modelled by the known scalars. An appropriate sliding surface function is firstly presented. Furthermore, some sufficient criteria via the free weighting matrices idea are obtained to ensure the admissibility of the resultant sliding motion by introducing new Lyapunov-Krasovskii functional. Subsequently, an RASMC law is synthesised to ensure the reachability criterion of pre-designed sliding surface, where an adaptive mechanism is introduced to estimate the related unknown bounds. Finally, the feasibility of the new RASMC strategy is illustrated by a numerical simulation.

This paper is concerned with the variance-constrained filtering problem for a class of discrete-time genetic regulatory networks (GRNs) with state delay and random one-step measurement delay. The phenomenon of the random one-step measurement delay is characterised by a random variable, which is assumed to obey the Bernoulli distribution with known occurrence probability. The purpose of the addressed problem is to design a filter such that, in the presence of state delay and random one-step measurement delay, an upper bound of the filtering error covariance matrix can be obtained and the explicit expression of the filter gain matrix is given. Then, the proposed variance-constrained filtering method can be used to approximate the concentrations of mRNAs and proteins. Finally, a numerical example is provided to illustrate the effectiveness of the designed filtering scheme.

The protocol-based memory fault detection (FD) problem under finite-time constraint is investigated for nonlinear networked systems, where the round-robin protocol is adopted to identify which sensor node can release the measured value at each transmission instant. In particular, the past states of the filter are exploited to develop the memory fault detection filter (FDF). Subsequently, the Finsler lemma and the Lyapunov approach are combined to analyze the finite-time stability of the addressed system. Then, the specific expression of the memory FDF gain matrices is obtained by using the solutions to certain matrix inequalities. In addition, for the aim of verifying that the memory FD approach has higher detection accuracy, a memoryless FDF is also designed in comparison with the memory FDF. In the end, the illustrative simulation studies are given to demonstrate the applicability of developed FD filtering algorithms in resistance–inductance–capacitance circuit system and the superiority of the designed memory FD scheme.

In this paper, the robust fault detection (RFD) problem is studied for uncertain networked systems with time delay and measurement outliers under limited communication condition, where the time delay is presumed to occur randomly and the occurrence probability is considered to be uncertain. Specifically, in order to reduce the communication burden, the stochastic communication protocol (SCP) is introduced to adjust the transmission of measurement signals. Moreover, a fault detection filter (FDF) with saturation constraints is constructed to achieve the purpose of properly eliminating possible measurement outliers. Subsequently, a generalized sector condition is utilized to derive the stability criteria of the system on the basis of appropriate Lyapunov functional. In addition, a traditional FDF is also designed to compare with the saturation-constrained FDF. It is shown that the FDF with saturation constraints can properly avoid the influence of outliers on the detection effect. Finally, three simulations are presented to show the superiority and the practicality of the developed saturation-constrained fault detection (FD) filtering algorithm.