No Excuses to Avoid Observing Unstable Nonlinear Systems: An LMI-Based Discontinuous Solution

• 成果类型: Article
• 署名作者: Quintana, Daniel; Estrada-Manzo, Victor; Bernal, Miguel
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3393838
• 发表日期: 2024
• 页码: 7136-7143
• 关键词: Observers; vectors; STANDARDS; PROPOSALS; Lyapunov methods; Linear matrix inequalities; stacking; Convex model; linear matrix inequality (LMI); nonlinear observer; sliding modes

摘要

A novel discontinuous observer design for nonlinear systems, whether stable or not, is presented in this article; it removes former limitations on matching and minimum-phase conditions, Lipschitz bounds, and linearity of outputs. Based on a pair of diffeomorphisms an observer error system can be written whose nonlinear nominal model depends entirely on the error, input, and output signals, thus allowing error-dependent domains of attraction where unstable signals are estimated. Nonlinear nominal models constitute the key for the proposal power and flexibility; they are handled via convex embedding of nonlinearities and the direct Lyapunov method. The discontinuous nature of the observer makes it insensitive to matched signals; the influence of unmatched terms is attenuated via H-infinity techniques. All design conditions are in the form of linear matrix inequalities. The examples illustrate the advantages over the existing methodologies even for unstable nonminimum-phase systems that do not hold the standard matching or Lipschitz conditions.