Design of full and reduced orders observers for linear fractional-order systems in the time and frequency domains

We propose a simple model of full and reduced linear “Luenberger-type” fractional-order observers for commensurate linear fractional-order systems in time and frequency domains, in the case where the measurements are not affected by disturbances. The design process of observers is determined from the solution obtained in time domain, the observer gains are computed by solving Linear Matrix Inequalities (LMI) following the fractional-order value (0 <; α <; 1 or 1 ≤ α <; 2) of system and ensure convergence of the observation error. The frequency procedure design is derived from time domain results with the aid of the factorization approach, where we define some useful coprime factorization. Then the linear fractional-order observers and their estimation error dynamics which are parametrized in the frequency domain.