Spectral Decomposition Methods for the Computation of RMS Values in an Active Suspension

The theory of the spectral decomposition of a matrix with distinct eigenvalues is reviewed briefly and then applied to the closed-loop system matrix of a quarter-car active suspension with preview. RMS values of the state variables and the control force are derived for an integrated white noise type random road input with the assumption of an optimised control system. The explicit formulæ obtained are easily computed numerically using MATLAB with accurate results at all speeds.