On Observability and Pseudo State Estimation of Fractional Order Systems

In this paper, fractional order system observability is discussed. A representation of these systems that involves a classical linear integer system and a system described by a parabolic equation is used to define the system real state and to conclude that the system state is approximately observable. However, it is also shown that the pseudo state space representation, usually encountered in the literature for fractional systems, can be used to design Luenberger like observers that permits an estimation of important variables in the system. Such an observer is finally used in order to estimate the temperature in a thermal system from a temperature measure at a different abscissa.