Stability of Non-Negative Lur'e Systems

Bill, Adam; Guiver, Christopher; Logemann, Hartmut; Townley, Stuart

Abstract

A stability/instability trichotomy for a class of nonnegative continuous-time Lur'e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute stability theory, and recent input-to-state stability results for Lur'e systems. Applications of the results derived arise in various fields, including density-dependent population dynamics, and two examples are discussed in detail.

Citation

Bill, A., Guiver, C., Logemann, H., & Townley, S. (2016). Stability of Non-Negative Lur'e Systems. SIAM Journal on Control and Optimization, 54(3), 1176-1211. https://doi.org/10.1137/140994599

• Journal Article Type: Article
• Acceptance Date: Jan 27, 2016
• Online Publication Date: May 12, 2016
• Publication Date: 2016
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Aug 11, 2020
• Journal: SIAM Journal on Control and Optimization
• Print ISSN: 0363-0129
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 54
• Issue: 3
• Pages: 1176-1211
• DOI: https://doi.org/10.1137/140994599
• Keywords: absolute stability, input-to-state-stability, Lur'e system, multiple equilibria, population modeling, positive systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2677318