Numerical derivation of fading-memory polynomial and sinusoidal filters for discrete-time control systems

Fading-memory polynomial (FMP) filters are useful as lag and lead compensators in control systems. It is shown that these recursive filters, with an infinite impulse response (IIR), need not be derived analytically using the orthogonal discrete Laguerre polynomials and that numerical matrix inversion is sufficient for low-order filters. This then enables the discounted least-squares approach, used in the design procedure, to be generalized to products of any family of weighting functions and any family of regressor functions (e.g. complex sinusoids), for which simple Z-transforms exist. In this introductory treatment, the fading-memory filters are derived and their use as lag and lead compensators is illustrated using simulation.