An Adaptive Observer with Exponential Rate of Convergence

Abstract

This paper is concerned with the design of an adaptive observer to estimate state variables and identify parameters of an unknown linear single-input single-output system with desired rate of exponential convergence. The observer structure is based on Kreisselmeier type representation of non-minimal realization, but in this study the adaptive law is obtained by a new scheme. The adaptive law is determined by equations forcing the errors into decreasing exponentially. That is, the adaptive observer is designed with the exponential rate of convergence in respect to parameter mismatches. The convergence rate is related on small number of parameters of the observer and the rate is specified arbitrarily. A sufficient condition for this property is obtained. An example is given to show the effectiveness of this design scheme.