Some critical properties of sign inverting control for LTI systems with multiple delays

A novel control logic, sign inverting control (SIC) is proposed for linear time-invariant multiple time delay systems (LTI-MTDS). SIC simply inverts the sign of a nominal control logic which is formulated for non-delayed dynamics using any known technique. The main objective of the inversion is to increase the delay robustness of the system. Three necessary and sufficient conditions are provided for SIC to be a viable option. This inversion method gains its strength from a recent paradigm called the Cluster Treatment of Characteristic Roots (CTCR). CTCR provides the necessary exact and exhaustive declaration of the stable regions in the domain of the delays for such systems. As the highlight of the paper, the spectral and root tendency invariance properties between the nominal and the SIC applied systems are presented with detailed proofs. Finally, we demonstrate an unexpected feature by an example, that SIC may also be applied to systems which are closed-loop non-delayed unstable for both control schemes.