Refinement of balancing order reduction techniques using Kessler´s formula

We present a methodology using Kessler´s formula that potentially improves the system order reduction techniques based on system balancing. The formula is simple and easy to use. We show how to refine the balancing order reduction techniques for single-input single-output systems by using Kessler´s formula that produces the equivalent time constant of the neglected part of the system. Using Kessler´s formula all the neglected stable system time constants, either fast or slow, can be approximated by only one time constant, which preserves valuable information about the neglected part of the system. The balancing truncation and residualization techniques can be improved by adding in parallel a first order equivalent fast system that approximates the neglected fast dynamics, and the reversed residualization techniques can be improved by adding in parallel a first-order slow system that approximates the neglected slow subsystem