Probing inputs for subspace identification

There is experimental evidence that the standard subspace methods (e.g. the N4SID method) perform poorly in certain conditions where the past signals (past inputs and past outputs) and future input spaces are nearly parallel. Based on an elementary numerical conditioning analysis, the paper describes a class of (system-dependent) input signals (called probing inputs) which lead to the worst possible conditioning of the identification problem. Numerical results are included demonstrating how these input signals may lead to a substantial deterioration of performance of the algorithms in some experimental conditions