Modulating Function‐Based Algebraic Observer for Conformable Fractional‐Order Systems

ABSTRACT We propose a finite‐horizon algebraic observer for conformable fractional‐order linear systems. The construction combines a conformable integration‐by‐parts identity with unitary modulating functions so that derivatives are transferred from noisy measurements to predesigned kernels and the current state is isolated at the right endpoint of the observation window. Under a conformable uniform strong observability assumption and a companion‐form transformation, the observer yields an explicit reconstruction formula together with weighted robustness bounds with respect to measurement noise and process disturbances. We also provide a sampled‐data realization with FIR‐like dot products and discuss a conformable–LTV lift that is useful for implementation. An example is provided of a numerical recovery of the state and validates the theoretical noise limits. The suggested framework is to extend integer‐order modulating‐function observers to conformable dynamics without the complexity of a complicated implementation structure.