Known time reversal methods consist of three steps which may be listed as (i) the recording of signals and (ii) the time reversing of the recorded signals, and (iii) the transmission of the time-reversed signals. The first and third steps of the above process are retained, but the second step is modified. The empirical signal is transformed to fit mathematical forms taught by the mathematics of singularity and catastrophe theory that ensure a structural stability to the waveforms that will be received, when the time reversed signals are transmitted again. This structural stability ensures robustness of the waveform and the predominant direction of the flux of energy of the waveform, and improves controllability of the location of the high magnitude regions of the energy flux despite limited knowledge of the exact properties of the medium. Applications to drug delivery in the brain, and geophysical applications are envisaged.