Supply chain systems are network systems with several subchains each of which consists of facilities and distribution entities (suppliers, manufacturers, distributors, and retailers), and thus such systems can be viewed as multiagent systems. Consensus or coordination of multiple subchains is crucial for a stable market supply, especially in the case of some subchains suffering from production interruption, or losing connection with others, which become isolated subchains in some time period due to irresistible reasons. Once some unspecified isolated subchains appear, the topology structure of the system will be changed, and thus the multiagent-based supply chain system can be modeled as a switched system. This paper aims to investigate the problem of ${H_\infty }$ consensus for multiagent-based supply chain systems under switching topology and uncertain demands. To achieve the consensus of the system, switching controller is designed in which both production rate and distributed consensus protocol are considered. Sufficient conditions are given such that the whole system reaches consensus and desirable attenuation of bullwhip effect with an average dwell time approach, which allows some subchains to be isolated in some time periods. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

A phenomenon, known as mixed-mode, occurs naturally in switched delay systems, and it makes the stability analysis for such systems a challenge, especially for the case of time-varying delays. This note aims to investigate the effects of mixed-modes on the stability analysis of switched time-varying delay systems, which are motivated from networked control applications. By constructing a Lyapunov-Krasovskii functional and using the estimation of quadrature, as well as the average dwell time approach, new exponential stability conditions are given for the switched time-varying delay systems with both stable and unstable subsystems. This can be seen as a generalization of existing results that mainly focus on the cases of constant delay and all stable subsystems. Finally, simulation examples are presented to illustrate the developed results.

Aiming at the real-time robust optimization problem of perishable supply-chain systems in complex environments, a real-time robust optimization scheme based on supply-chain digital twins is proposed. Firstly, based on the quantitative logical relationship between production and sales of single-chain series supply-chain system products, the state space equation of the supply-chain system with logical characteristics, structural characteristics, and quantitative characteristics was constructed, and twin data were introduced to construct the digital twins of supply chains based on the state-space equation. Secondly, the perishable supply-chain system in complex environments was regarded as an uncertain closed-loop system from the perspective of the state space equation, and then a robust $H_{\infty }$ controller design strategy was proposed, and the supply-chain digital twins was used to update and correct the relevant parameters of the supply-chain system in real-time, to implement the real-time robust optimization based on the supply-chain digital twins. Finally, the simulation experiment was carried out with a cake supply-chain production as an example. The experimental results show that the real-time updating of relevant parameters through the digital twins can help enterprise managers to formulate reasonable management plans, effectively avoid the shortage problem of enterprises in the cake supply-chain system, and reduce the maximum inventory movement standard deviation of each link by 12.65%, 6.50%, and 14.87%, and the maximum production movement standard deviation by 70.21%, 56.84%, and 45.19%.