Conditioned diffusion models have demonstrated state-of-the-art text-to-image synthesis capacity. Recently, most works focus on synthesizing independent images; While for real-world applications, it is common and necessary to generate a series of coherent images for story-stelling. In this work, we mainly focus on story visualization and continuation tasks and propose AR-LDM, a latent diffusion model auto-regressively conditioned on history captions and generated images. Moreover, AR-LDM can generalize to new characters through adaptation. To our best knowledge, this is the first work successfully leveraging diffusion models for coherent visual story synthesizing. It also extends the text-conditioned method to multimodal conditioning. Quantitative results show that AR-LDM achieves SoTA FID scores on PororoSV, FlintstonesSV, and the adopted challenging dataset VIST containing natural images. Large-scale human evaluations show that AR-LDM has superior performance in terms of quality, relevance, and consistency. Code available at this https URL

This paper is concerned with the stability and stabilization of delayed discrete-time T-S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. Firstly, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov-Krasovskii functional, using the proposed inequality to estimate its forward difference, and using a cubic functional negative-determination lemma to handle non-convex conditions with respect to the delay, a delay and its variation dependent stability criterion is obtained. Moreover, the corresponding controller design method for the closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches.

The exponential extended dissipativity for delayed discrete-time neural networks (DTNNs) is researched in this paper. The considered time-varying delays have distinctly larger values in intermittent time periods (named as large delay periods (LDPs)) than other time periods. Firstly, the DTNN with LDPs is modeled as a switched system with two subsystems. Then, the definition of exponential extended dissipativity is proposed, which reflects the relationship between the extended dissipativity performance and exponential decay rate. By using the proposed definition, constructing an augmented switched Lyapunov functional with LDP-based terms and using inequalities to estimate its forward difference, the criterion for guaranteeing the DTNNs to be exponentially extended dissipative is obtained. Moreover, the corresponding stability condition is obtained when the external disturbance is zero. Finally, three numerical examples are given to demonstrate the merits of wider applications and less conservatism of the proposed methods.

The stability and ${\mathcal {H}}_\infty$ filtering for delayed discrete-time T–S fuzzy systems are studied in this paper. The primary objective is to obtain less conservative and more effective analysis and design methods by exploring a combination of the characteristics of T–S fuzzy systems and the delay-dependent methods. First, as the first step of the Lyapunov-Krasovskii functional (LKF) method, a membership-dependent (MD) LKF with delay-product-type term is established to contain more delay and membership function information. Then, to obtain the negative definite condition of the forward difference of the constructed functional, an MD-matrix-separation-based inequality is developed to obtain tighter estimations for the augmented summation terms and an MD-variable-augmented-based free-weighting matrix method is proposed to avoid the generation of delay-dependent nonlinear terms. Based on the above methods, a less conservative stability criterion and an ${\mathcal {H}}_\infty$ fuzzy filter design method are proposed. Finally, the merits of the proposed methods are verified via two examples.