An improved adaptive observer design for a class of linear time-varying systems

In previous studies on adaptive observers for linear time-varying (LTV) systems, the provided results were commonly based on a strong assumption that there exists a time-varying feedback gain matrix F(t) stabilizing the pair (A(t), C(t)). However, in general, it is a difficult task for LTV system (A(t), B(t), C(t)). In this note, we apply an improved high gain observer to the design of adaptive observers for a class of LTV systems with uncertain parameters. The proposed observer removes the difficulty of finding F(t) by using a time-varying high-gain matrix, where only a constant parameter and a constant matrix need to be designed. Through a transformation for the error dynamics, it shows that the estimated errors are globally exponentially convergent. Finally, an illustrative example is included to show the validity of the design approach.