Analysis of spline based auxiliary signal design for failure detection in delay systems

In an active approach for model detection and its use in failure detection, an auxiliary control is applied in order to assist in model identification. An active approach for robust multi-model identification and failure detection in the presence of disturbances over possibly short time intervals has been introduced. Previous papers extended the original design procedure to problems with several delays and additive noise. The infinite dimensional delay problem was approximated by a finite dimensional system without delays and numerical examples were worked. The numerical examples seemed to converge better than was expected. In this paper we explain that convergence. In addition we discuss the extension of the previous results for delay systems with additive noise to those with small model uncertainties and explain why this additional assumption of small uncertainty, which was not present in the case without delays, is now needed for the analysis.