Extended Observer Forms for Submersive Discrete-Time Systems

• 成果类型: Article
• 署名作者: Simha, Ashutosh; Kaparin, Vadim; Mullari, Tanel; Kotta, Ulle
• 署名单位: Delft University of Technology; Tallinn University of Technology; Tallinn University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3336253
• 发表日期: 2024
• 页码: 2684-2688
• 关键词: Observers; Output feedback; nonlinear dynamical systems; MANIFOLDS; discrete-time systems; Transforms; STANDARDS; discrete-time system; extended observer form; geometric methods; nonlinear observers

摘要

This technical note addresses the problem of transforming a single-input-single-output discrete-time system into the extended observer form, which comprise a linear time-invariant observable component, and a nonlinear injection term, which depends on the input, output, and their forward shifts up to a finite order. Intrinsic necessary and sufficient conditions are provided for obtaining the extended observer form via a parametrized state transformation. The conditions are formulated directly in terms of the state equations and do not rely on input-output equations as in the earlier papers. Further, an algorithm for obtaining the required transformation is presented. Unlike the existing results on observer forms, the results are not restricted to reversible systems but to more general submersive systems, i.e., to systems, which are reversible via static state feedback.