Unknown input observer design for OSL <i>ς</i> ‐tempered fractional‐order systems

Abstract This paper addresses the design of an unknown input observer for fractional‐order systems characterized by one‐sided Lipschitz nonlinearities. The proposed observer ensures robust state estimation in the presence of unknown disturbances and time‐varying inputs. By leveraging tempered fractional calculus and Lyapunov stability theory, sufficient conditions for ‐Mittag‐Leffler stability are derived and formulated as linear matrix inequalities, solvable via standard numerical tools. A simulation case study on a 3D fractional‐order system demonstrates the observer's effectiveness in reconstructing unmeasured states and rejecting unknown disturbances. The work generalizes existing observer design methodologies to fractional‐order dynamics, offering enhanced applicability to systems with nonlocal and memory‐dependent properties.