A digital input/output model for trace-class systems

AbstractThis paper derives an input/output representation for infinite dimensional linear systems whose state transition operators are trace-class. The representation is an infinite dimensional autoregressive moving-average (ARMA) model whose coefficients are shown to decay faster than exponentially. The relationship between this ARMA model and the initial-value problem for an infinite dimensional state-space representation of the same system is established. It is shown that if a one-step-ahead output predictor is based on the infinite dimensional ARMA model, the predicted output will approach the output from the state-space initial-value problem faster than exponentially