Stability analysis and controller design for the heat equation with time delayed feedback

Abstract

In this thesis, the stability analysis for the system defined by the heat equation with time delayed feedback is performed. In the first part of the thesis, stability conditions in terms of LMI conditions which are obtained from the analysis in time domain, are explained. Necessary and sufficient conditions for stability are obtained using a frequency domain analysis. In the second part of the thesis, robust stability conditions are obtained for the system with parametric uncertainty. In the third part, an 퐻∞ controller design procedure is given for this type of plants described by the heat equation with time delayed feedback. Finally, the results are illustrated with simulations.