Unified Observer Design Framework for Time-Varying Systems With Delays and Parameter Uncertainty

This paper presents a unified framework for designing observers for time-varying systems with time delays and parameter uncertainties. The considered delays are discrete and distributed nature, entering both the state and output equations. Parameter uncertainties also come in both equations. Doing so, the present system formulation turns out to be a generalization of existing works. The problem of observer design is dealt by using an approach that combines a Kalman-like design for time-varying systems and a decoupling transformation that makes state estimator design decoupled from parameter estimator design. The adaptive observer obtained this way contains a (Kalman-like) state estimator, a parameter estimator, and an auxiliary filter. In the case where the output equation is subject only to discrete delay, we design an adaptive observer that includes, in addition to the previous components, an output predictor that allows to better compensates for the delay effect. Both observers are shown to be exponentially stable under well-defined conditions ensuring system observability and persistent excitation (PE). In the absence of distributed output delay, the predictor-based observer accommodates much larger delays, compared to the predictor-free observer.