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Abstract Global sampled‐data stabilization for a class of nonlinear continuous system with input delay has been investigated directly in the discrete‐time domain due to challenges confronted in dealing with infinite‐dimensional system under input delay. Memorized state feedback controllers and output feedback controllers based on dynamic extension of state space have been constructed within the framework of co‐design between sampling period and scaling gain. Upon this compensation scheme, global sampled‐data stabilization a class of nonlinear system has been successfully realized no matter the input delay is smaller than the sampling period or not. Compared with memory‐less sampled‐data controllers, not only sampled‐data stabilization under large input delay has been realized but also transient performance of closed‐loop system has been further improved. Simulation results under different input delays and sampling periods have illustrated the effectiveness of results obtained.

Abstract Background Macrophages show versatile functions in innate immunity, infectious diseases, and progression of cancers and cardiovascular diseases. These versatile functions of macrophages are conducted by different macrophage phenotypes classified as classically activated macrophages and alternatively activated macrophages due to different stimuli in the complex in vivo cytokine environment. Dissecting the regulation of macrophage activations will have a significant impact on disease progression and therapeutic strategy. Mathematical modeling of macrophage activation can improve the understanding of this biological process through quantitative analysis and provide guidance to facilitate future experimental design. However, few results have been reported for a complete model of macrophage activation patterns. Results We globally searched and reviewed literature for macrophage activation from PubMed databases and screened the published experimental results. Temporal in vitro macrophage cytokine expression profiles from published results were selected to establish Boolean network models for macrophage activation patterns in response to three different stimuli. A combination of modeling methods including clustering, binarization, linear programming (LP), Boolean function determination, and semi-tensor product was applied to establish Boolean networks to quantify three macrophage activation patterns. The structure of the networks was confirmed based on protein-protein-interaction databases, pathway databases, and published experimental results. Computational predictions of the network evolution were compared against real experimental results to validate the effectiveness of the Boolean network models. Conclusion Three macrophage activation core evolution maps were established based on the Boolean networks using Matlab. Cytokine signatures of macrophage activation patterns were identified, providing a possible determination of macrophage activations using extracellular cytokine measurements.