Wavelet-based identification of fast linear time-varying systems using function space methods

The present work proposes a rigorous general framework and a rapidly convergent identification algorithm for high speed identification of fast linear time-varying systems on short time intervals. The identification speed-up is attained via utilizing both time and frequency localized bases. This feature permits identification of fewer coefficients without noticeable loss of accuracy of the identification results. Under an assumption that the inputs and outputs of the plants considered in the present work belong to l^p spaces, where p = 2 or p = ∞, their impulse responses are shown to belong to Banach spaces. Further on, by demonstrating that the set of all BIBO systems is a Banach space, the system modeling and identification are shown to be reducible to linear approximation problems in a Banach space setting. Simulation shows that the resulting identification algorithms can reject small persistent random disturbances as well as generate the short-term spiky descriptions of fast linear time-varying systems with nonsmooth coefficients.