SOS for Systems with Multiple Delays: Part 2. H∞-Optimal Estimation

Matthew M. Peet, Keqin Gu

Abstract: In this paper, we develop an SOS-based approach for design of observers for time-delay systems. The method is an extension of recently developed algorithms for control of infinite-dimensional systems. The observers we design are more general than the class of observers most commonly associated with time-delay systems in that they directly correct both the estimate of present state and the history of the state. As a result, the observer is itself a PDE. In this case the traditional notions of strong and weak observability do not apply and the resulting observer-based controllers can significantly outperform existing approaches.