An adaptive scheme for delay estimation in fractional order systems

With reference to linear time invariant fractional-order systems, of both commensurate and non-commensurate type, a novel, gradient-based, procedure for the adaptive estimation of the delay parameter is presented in the current paper. The connections between the proposed delay estimation algorithm and a recently proposed technique for commensurate order estimation are highlighted and discussed. The algorithm is supported by an appropriate Lyapunov-based stability analysis providing sufficient convergence conditions. Simulation examples are presented to show the correct functioning of the scheme.