**DOI** https://doi.org/10.1016/j.sysconle.2018.05.011

**Scientific Field** Computer science, Mathematics and Mathematical physics

**Fellow**Prof. Yiming Chen re

## ABSTRACT

In this paper, a non-asymptotic pseudo-state estimator for a class of commensurate fractional order linear systems is designed

in noisy environment. Different from existing modulating functions methods, the proposed method is based on the system

model with fractional sequential derivatives by introducing fractional order modulating functions. By applying the fractional

order integration by parts formula and thanks to the properties of the fractional order modulating functions, a set of fractional

derivatives and fractional order initial values of the output are analogously obtained by algebraic integral formulas. Then,

an explicit formula of the pseudo-state is accomplished by using the fractional sequential derivatives of the output computed

based on the previous results. This formula does not contain any source of errors in continuous noise-free case, and can be used

to non-asymptotically estimate the pseudo-state in discrete noisy case. The construction of the fractional order modulating

functions is also shown, which is independent of the time. Finally, simulations and comparison results demonstrate the efficiency

and robustness of the proposed method