New observer and state estimates to nonlinear systems with real-order derivatives

The problem of constructing an observer system to nonlinear systems with real-order derivatives seems a very new issue in advanced control theory. This paper considers real-order derivative systems associated with time-dependent coefficients and different orders in (0,1], and the random initial-time lying in the real number line. We implement the known idea of linear nonhomogeneous time-varying controller and provide an approach that can be used to design an observer for such systems. We develop new comparison results that give order-dependent criteria in order to construct observers for such systems. It is found that the Metzler matrix and a non-negative matrix play an important role in the analysis of observers and state estimates of such systems.