An adaptive observer and identifier with an arbitrarily fast rate of convergence

Based on the implementation and the method of approach, the adaptive observers are herein classified as explicit and implicit observers. Both types are discussed from a convergence point of view, and a geometrical interpretation of the adaptive algorithms is given in order to account for their slow rate of convergence. Finally, an improved adaptive observer is formulated for nth order, linear, single-output, observable and time invariant systems. The proposed scheme uses only input and output measurements, is globally asymptotically stable and has an arbitrarily fast rate of convergence for both the system state and the system parameters. Simulation results are included.