Reduced-order adaptive observer for rectangular descriptor systems with incremental quadratic constraints

Meenakshi Tripathi, Lazaros Moysis, Mahendra Kumar Gupta and Christos Volos

International Journal of Systems Science, 2026, vol. 57, issue 3, 842-856

Abstract: This paper investigates the challenge of reduced-order adaptive observer design for nonlinear rectangular descriptor systems. Nonlinearities satisfying incremental quadratic constraints are explored that cover Lipschitz, one-sided Lipschitz, monotone, and many other nonlinearities. The complexity of the problem lies in the presence of unknown parameters in the nonlinear part of the system that have to be estimated along with system states simultaneously. Orthogonal transformations reduce the system to an equivalent form that contains nonlinearities in the output. Under certain rank assumptions, the observer's existence conditions are simplified as an adaptation law, a set of algebraic constraints, and the solvability of a linear matrix inequality. A numerical simulation is provided to illustrate the findings.

Date: 2026
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DOI: 10.1080/00207721.2025.2514590

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