Generalization of Adaptive Observer and Method of Optimizing Its Convergence Properties

This paper concerns a generalization of the design of the adaptive observer, and an investigation of its convergence properties. By application of hyperstability theory the design freedom is enlarged to permit use of time variable adaptive gains. Based on the assumption of periodic excitation, and with the aid of Floquet Theory a new convergence criterion is defined. By this means the effects of adaptive gains and input frequencies upon convergence time are evaluated. Structural properties of the adaptive observer are compared with other adaptive schemes, in particular with regard to bias due to noise.