## 1 Introduction  
The dynamics of most practical systems are inherently nonlinear due to complex physical, chemical and biological mechanisms. The modeling of nonlinear systems is challenging and has become an active research area in both academia and industry [1; 2]. To simplify the modeling problem, block-oriented models, which are composed of linear dynamic blocks in combination with nonlinear memoryless blocks, have been widely utilized to describe nonlinear systems. The state of the art in designing, analyzing and implementing identification algorithms for block-oriented nonlinear systems were well summarized in a recent book by [PERSON] and [PERSON] [3]. Depending on the location of the static nonlinear component, block-oriented models can be classified into the Hammerstein model, the Wiener model and the Hammerstein-Wiener model [4; 5; 6]. The Hammerstein model represents a class of input nonlinear systems, where the nonlinear block is prior to the linear one. It can flexibly approximate various input nonlinearities, such as saturation, dead zone, backlash and hysteresis, thus having been extensively employed in realistic applications [7; 8; 9; 10; 11]. For decades, the identification of Hammerstein nonlinear systems has attracted much attention, and numerous methods have been reported in the literature. For example, [PERSON] et al. studied the parameter estimation of Hammerstein systems where the linear part is described by an output error model and presented an iterative algorithm based on the optimal bounding ellipsoid criterion [12]. [PERSON] et al. applied the auxiliary model identification principle to deal with unmeasurable noise-free outputs in Hammerstein output error systems, presented a recursive least squares (RLS) algorithm and investigated its convergence properties [13]. [PERSON] derived a robust extended RLS algorithm to estimate the parameters of Hammerstein systems interfered by non-Gaussian disturbance [14]. [PERSON] et al. proposed a blind identification algorithm for Hammerstein systemswith hysteresis nonlinearity and further developed a composite control strategy to track the reference input [15]. Among various new methodologies in the identification area, the multi-innovation theory has been considered as a useful way to improve estimation precision and convergence rate. The basic idea of the multi-innovation theory is innovation expanding, which helps to update the parameter estimates at each recursion using the data over a moving and fixed-size window [16; 17]. Typically, the multi-innovation theory is incorporated with the RLS algorithm, the stochastic gradient (SG) algorithm, the stochastic Newton recursive algorithm, etc., to address identification problems [18]. For instance, a multi-innovation RLS algorithm was developed for Hammerstein AutoRegressive eXogenous (ARX) systems with backlash nonlinearity [19]. Furthermore, a multi-innovation SG algorithm [20] and an auxiliary model-based multi-innovation generalized extended SG algorithm [21] were proposed to estimate the parameters of Hammerstein nonlinear ARX and Box-Jenkins systems, respectively. Compared with the multi-innovation RLS algorithm, the multi-innovation SG algorithm is more efficient in computation because it avoids performing large matrix inversion [22]. The above-mentioned Hammerstein systems all belong to single-rate systems, the inputs and outputs of which are uniformly sampled at the same rate. However, non-uniform sampling can be encountered in practice due to hardware limitations or economic considerations [23; 24; 25]. For example, influenced by transmission delays and packet losses, the input-output data in networked control systems might be available at non-uniformly spaced time instants [26; 27]. The non-uniform sampling includes the uniform sampling as its special case, which can always preserve controllability and observability in discretization [28]. Furthermore, it can overcome the restriction of the Nyquist limit and enable a much lower average sampling frequency.