A Toolkit for Globally Robust Observer-Based Feedback With Relaxed Characterization of iISS/ISS

• Published in: IEEE transactions on automatic control Vol. 68; no. 7; pp. 3858 - 3871
• Main Authors: Ito, Hiroshi, Shim, Hyungbo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Closed loops; Control systems; Couplings; Error analysis; Estimation error; Feedback control; Flexibility; Integral input-to-state stability; Lyapunov functions; Measurement uncertainty; Noise measurement; Observers; Output feedback; output feedback control; Robustness; small gain theorem; Toolkits
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3193270

This article elaborates on flexibility in dealing with the interconnection of integral input-to-state stable (iISS) and input-to-state stable (ISS) systems. The undecoupled characterizations introduced separately for iISS and ISS in the literature are linked to build a framework enabling global analysis without settling for local and semiglobal properties. Feedback control design in the presence of measurement noise can benefit from the framework immediately if plants are nonlinear, irrespective of application areas. This article proposes a toolkit for providing robustness guarantees in observer-based output feedback control subject to measurement noise. For a nonlinear plant, the couplings among the plant state, the estimation error, and the measurement noise arising in the closed-loop equations often hinder global analysis, such as ISS with respect to the measurement noise. In the formalism of iISS, this article demonstrates that the flexibility in dealing with the couplings allows one to establish the robustness globally. Moreover, it gives a condition under which the closed-loop system can possess ISS and strong iISS, which are stronger than iISS.