H∞ observer design for linear fractional-order systems in time and frequency domains

In this paper, the problem of robust fractional-order observer (RFO) design in time and frequency domains for disturbed fractional-order system is investigated. The main results include the formulation of robust observer design problems in time and frequency domains. In the time domain, we develop a sufficient condition for the existence of a robust observer design, and its construction is based on the Linear Matrix Inequalities (LMI) formulation. The frequency procedure design is derived from time domain results with the aid of the factorization approach, where we define some useful coprime factorization. An illustrating example is presented to demonstrate the effectiveness of the proposed approach.