Algebraic linear matrix inequality design of robust sensor fault estimators for ς$$ \varsigma $$‐tempered fractional‐order systems with monotone nonlinearities

Abstract This paper presents a robust sensor fault estimation (RSFE) approach for ‐tempered fractional‐order systems with monotone nonlinearities. Building on an algebraic framework for observer design, the proposed method extends the conventional Caputo derivative to a tempered fractional derivative setting. The design incorporates a nonlinear unknown input observer and algebraic adaptation laws that rigorously guarantee ‐Mittag‐Leffler stability ( ‐MLS). Simulation studies confirm the observer's effectiveness in estimating sensor faults under unknown disturbances and nonlinear dynamics, validating both the algebraic stability criteria and practical applicability. The results demonstrate that the algebraic formulation reduces conservatism compared to classical Lyapunov‐based approaches, particularly for tempered fractional operators with memory effects.