Fractional error model 1 in adaptive systems

This paper presents the analysis of Error Model 1 when 0 <; α <; 1, in the context of Fractional Adaptive Systems. Simulation studies are presented, which show the main characteristics of this error model, from stability and error convergence point of view, as well as the main characteristics of the errors transient response. The stability of the Error Model is proved using the Lyapunov direct method for fractional systems, and the main difficulties that arise in the convergence analysis of the errors are discussed.