Stability Analysis of the Heat Equation with Time-Delayed Feedback

In this paper we consider the heat equation with time delayed feedback. Recently, stability analysis of this system, with possibly time-varying delay, is done by Fridman and Orlov (2007, 2009); and a sufficient condition is obtained for stability in terms of a linear matrix inequality Here we consider the same system, but with constant delay, and perform the stability analysis in the frequency domain. A necessary and sufficient condition is obtained in terms of the system parameters. The result is illustrated with numerical examples.