Passivity analysis and synthesis for uncertain time‐delay systems
Magdi S. Mahmoud, Lihua Xie · Mathematical Problems in Engineering · 2001
In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time‐delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time‐delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay‐independent and delay‐dependent cases are considered. For the synthesis problem, we propose an observer‐based design method which guarantees that the closed‐loop uncertain time‐delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.