Minimal order arbitrarily fast adaptive observers and identifiers

A general description of the implicit adaptive observer [13] is presented which defines the interrelationship between the different adapfive observers that have been reported in literature. Within the framework of the general formulation, two schemes are proposed to synthesize multierror adaptive observers for nth order, linear, single-output, observable and time-invariant systems with improved convergence characteristics. The proposed schemes use only input and output measurements, are globally asymptotically stable and have an arbitrarily fast rate of exponential convergence for both the system parameters and the system state. If all system parameters are unknown, the second scheme is the minimal order observer that can afford arbitrarily fast exponential convergence. Simulation results are included.