Practical Observer Design for a Class of Tempered Fractional‐Order Systems

This manuscript deals with designing a practical observer for a distinguished class of tempered fractional‐order systems (TFOS). Tempered fractional calculus modifies classical fractional operators by incorporating an exponential tempering factor, which allows correct modeling of systems that exhibit fading memory while preserving the inherently nonlocal nature of fractional dynamics. In this paper, we propose an observer architecture for nonlinear TFOS subject to a disturbed Lipschitz condition and derive sufficient stability criteria using Lyapunov analysis and free‐weighting matrices, resulting in linear matrix inequalities (LMIs) based on a quadratic Lyapunov function. The main result is the practical generalized Mittag‐Leffler stability of the estimation error, which explicitly depends on the fractional order and the tempering parameter. The efficacy and robustness of the proposed approach are demonstrated through a numerical example.