## 1 Introduction  
In circuit theory, the memristor is the fourth novel passive nano-information device, after the three basic circuit components of inductor, capacitor and resistor, which has the functions of memory and resistance. Studies have found that the memory characteristics of memristor can reflect well the excitation and inhibition of synapses in artificial neural networks (ANNs) [1]. Therefore, memristive neural networks (MNNs), which utilize the memristor to replace the synapse in the ANNs, have attracted the extensive attention of scholars. MNNs are extensively employed in intelligent control, signal processing, pattern recognition, etc. Nonetheless, with increasing network size and complexity, various faults and disturbances may occur in MNNs. If these faults and disturbances are not promptly estimated to make the system adjust as early as possible, the performance of the MNNs will decay or even collapse. Therefore, the state estimation of MNNs has gained some attention from academic research communities. For example, corresponding estimation approaches have been designed to estimate various MNNs, such as random delayed MNNs [2], Markov switching MNNs [3] and proportional delayed complex-valued MNNs [4]. Dealing with the state estimation problem has two main kinds of approaches, namely, filter and observer. Among them, the filter has been widely used in the state estimation domain related to MNNs owing to its superior noise resistance [5; 6]. Different filtering strategies need to be selected for the different types of noise. Currently, most of the literature on filtering only considers white Gaussian noise and energy-bounded noise in MNNs. White Gaussian noise obeys the Gaussian distribution, and the primary processing techniques include recursive filtering [7], particle filtering [8], etc. Energy-bounded noise has bounded energy, and the primary processing techniques include \(H_{\infty}\) filtering [9], energy-to-peak filtering [10], etc. However, system operation may generate unknown but bounded (UBB) noise in reality, such as electromagnetic systems that can produce the UBB noise in electrical engineering, which does not follow either the assumption of a Gaussian distribution or bounded energy. For UBB noise, the traditional state estimation approaches become no longer applicable. Therefore, the set-membership filtering (SMF) was proposed to deal with these kinds of noises [11]. Compared to other filters, the SMF only requires a strict boundary constraint on noise rather than statistical characteristics and can give a group of ellipsoid sets that encompass all possible actual states with a 100% confidence degree. There have been many research results on using SMF to deal with UBB noise. For example, in response to the following various systems with UBB noise, such as multi-sensor network system [12], distributed nonlinear discrete system [13], time-varying system [14], nonlinear system [15] and event-triggered complex networks [16], the corresponding set-membership estimation schemes have been designed to estimate the state of the above systems. In an actual engineering scenario, ref. [17] has proposed a control scheme based on SMF to tackle the heading tracking control problem in an unmanned surface vessel (USV) affected by UBB noise, which guarantees the asymptotic stability of the USV systems. In [18], an SMF has been proposed to track the running trajectory of automatic guided vehicle (AGV) under UBB noise, which decreases the requirement for sensor precision. From the above, we can see that there have been some good research results on SMF. What is noteworthy is that the existing research has not considered some special practical problems fully, such as the uncertainty problems in engineering scenarios. In fact, in real engineering application scenarios, estimation performance is unavoidably influenced by uncertainties such as actuator degradation, numerical calculation errors and the aging of components.