Sliding mode observers for set-valued Lur’e systems with uncertainties beyond observational range

• Published in: Communications in nonlinear science & numerical simulation Vol. 140; p. 108325
• Main Authors: Adly, Samir, Huang, Jun, Le, Ba Khiet
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2025
• Subjects: Set-valued Lur’e systems; Sliding mode observer; Uncertainties outside the observation subspace; 93D20; Set-valued Lur’e systems; 34A36; 49J53; 49J52; 28B05; Sliding mode observer; Uncertainties outside the observation subspace; 34A60
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.108325

In this paper, we introduce a new sliding mode observer for Lur’e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard range of observation. Traditionally, most ofLuenberger-like observers and sliding mode observer have been designed only for uncertainties in the range of observation. Central to our approach is the treatment of the uncertainty term which we decompose into two components: the first part in the observation subspace and the second part in its complemented subspace. We establish that when the second part converges to zero, an exact sliding mode observer for the system can be obtained In scenarios where this convergence does not occur, our methodology allows for the estimation of errors between the actual state and the observer state. This leads to a practical interval estimation technique, valuable in situations where part of the uncertainty lies outside the observable range. Finally, we show that our observer is also a T-observer as well as a strong H∞ observer. •Sliding-mode observer: Introduction of a new sliding-mode observer for Lur’e definite-valued dynamical systems with uncertainties outisde the standard observational range. uncertainties.•Practical interval estimation: Development of a practical interval estimation technique for scenarios where uncertainties lie outside the observable range.•Exact observer: Prove that the observer is exact when the unobservable uncertainty component converges to zero over time.•Enhanced observability: Prove that the observer is both a T observer and a strong H∞ observer, providing robuste and accurate state estimates.