Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 28, Issue 7, Pages 1710-1715Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2016.2533392
Keywords
mu-stability; nonlinear; positive systems; time delay; unbounded
Categories
Funding
- National Science Foundation of China [61273211, 61203149, 61233016]
- National Basic Research Program of China (973 Program) [2010CB328101]
- Chen Guang Project through the Shanghai Municipal Education Commission
- Shanghai Education Development Foundation [11CG22]
- Fundamental Research Funds for the Central Universities
- Program for Young Excellent Talents in Tongji University
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The stability of the zero solution plays an important role in the investigation of positive systems. In this brief, we discuss the mu-stability of positive nonlinear systems with unbounded time-varying delays. The system is modeled by the continuous-time ordinary differential equation. Under some assumptions on the nonlinear functions, such as homogeneous, cooperative, and nondecreasing, we propose a novel transform, by which the nonlinear system reduces to a new system. Thus, we analyze its dynamics, which can simplify the nonlinear homogenous functions with respect to the arbitrary dilation map to those with respect to the standard dilation map. We finally get some new criteria for the global mu-stability taking the degree into consideration. A numerical example is given to demonstrate the validity of obtained results.
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