Dr. Liu is currently a tenured Assistant Professor in INSA (French National Institute of Applied Sciences) Centre Val de Loire, where he belongs to Control Team in PRISME Laboratory. Dr. Liu’s main research interests concern with estimation and identification for integer order and fractional order systems, such as numerical differentiation and parameter estimation. Until now, he has published more than 40 papers in international journals and conferences such as IEEE Transactions on Automatic Control, Automatica, SIAM Journal on Scientific Computing and Systems & Control Letters, etc. This talk aims at designing a non-asymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky's observable canonical form of pseudo-state space representation with unknown initial conditions. First, this form is expressed by a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output, based on which the modulating functions method is applied. Then, the former initial values and the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to non-asymptotically estimate the pseudo-state of the system in noisy environment. Second, the pseudo-state estimator is studied in discrete noisy case, which contains the numerical error due to a used numerical integration method, and the noise error contribution due to a class of stochastic processes. Then, the noise error contribution is analyzed, where an error bound useful for the selection of design parameter is provided. Finally, numerical examples illustrate the efficiency of the proposed pseudo-state estimator, where some comparisons with the fractional order Luenberger-like observer and a new fractional order H∞-like observer are given.