Asymptotic Results of H∞-Gain-Based Observers

• Published in: Journal of the Institution of Engineers (India). Series B, Electrical Engineering, Electronics and telecommunication engineering, Computer engineering Vol. 103; no. 4; pp. 1041 - 1046
• Main Authors: Verma, Reshma, Raol, Jitendra R.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.08.2022; Springer Nature B.V
• Subjects: Asymptotic properties; Communications Engineering; Dynamic stability; Dynamical systems; Engineering; H infinity; Kalman filters; Matlab; Networks; Nonlinear dynamics; Nonlinear systems; Observers; Original Contribution; Performance measurement; Robustness (mathematics); Loss of observations; Stability results; Delayed states; gain-based observers
• ISSN: 2250-2106; 2250-2114
• DOI: 10.1007/s40031-022-00727-5

Hither to H-Infinity theory has been utilized to develop robust estimators for dynamic systems, but so far it has not been considered to develop observers for nonlinear dynamic systems with state delays and loss of measurement data. In this paper, some theoretical results of H ∞ -gain (HI, H -Infinity)-based observers are devised. The Lyapunov energy (LE) function is used for obtaining stability results for these proposed observers’ error dynamics. First, HI-gain-based observer for conventional dynamic system is presented (as a first observer) and its asymptotic results derived; then, similar exercise is carried out for the system with delayed state and with loss of measurement data. (This is the second observer.) The second observer’s performance results are obtained using MATLAB implementation, which in turn establishes the derived convergence results of the second observer; and by induction, this would also establish the validity of the theoretical results for the first observer. This exercise is a novel contribution in the areas of observer theory, Kalman filtering, and HI theory and paves a way of synergy amongst these seemingly different approaches. The simulation-based performance results, presented in the forms of MATLAB plots and numerical error performance metrics, for the delayed state and loss of the measurements data are very encouraging.