Strong left-invertibility and strong input-observability of nonlinear time-delay systems

• Published in: IEEE control systems letters Vol. 7; p. 1
• Main Authors: Chen, Yahao, Ghanes, Malek, Barbot, Jean-Pierre
• Format: Journal Article
• Language: English
• Published: IEEE 01.01.2023
• Subjects: Automatic; Control systems; Delays; Engineering Sciences; Heuristic algorithms; input-observability; left-invertibility; nonlinear systems; Observability; structure algorithm; Symbols; Terminology; time delays; Transfer functions
• ISSN: 2475-1456; 2475-1456
• DOI: 10.1109/LCSYS.2022.3227130

In this paper, we study the problem of unknown inputs reconstruction for nonlinear time-delay systems. First we define two notions called strong left-invertibility and strong input-observability and the word "strong" is to address the causality properties of those two notions. Then necessary and sufficient conditions for the strong left-invertibility and the strong input-observability are given under the algebraic framework proposed in 1. We find that a sequence of inputs submodules plays an important role for the strong left-invertibility of time-delay systems. A structure algorithm is provided to construct that sequence and to formulate an input reconstructor. At last, several examples are given to illustrate how to check the strong left-invertibility and the strong input-observability by applying the proposed structure algorithm, and to show how to recover the inputs via causal outputs and the initial value functions of states (strong left-invertibility) or only via causal outputs (strong input-observability).