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The stability of linear time‐delay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature causes usually the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained either based on extensions of classical tests applicable to delay‐free systems or on approaches within the framework of two‐dimensional digital filters. Some of those two‐dimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems which involve coupled continuous and digital substates after a slight “ad‐hoc” adaptation of the tests for that situation.

The paper aims to propose a new method for estimating the time of arrival (TOA) of ultra-wideband (UWB) signals under IEEE 802.15.4a multipath channel model.

The proposed approach is based on a proportionality test and consists in finding out whether two autoregressive (AR) processes, modeling two frames, are proportional or not. The latter operation uses a distance to measure the proportionality between the two AR processes.

The developed technique may be used in two ways, sample-by-sample or block-by-block, according to the required ranging accuracy. It is important to note that the method offers flexibility between the computational load and the needed estimation accuracy. Moreover, the proposed method uses a threshold that is derived analytically according to a preset false alarm probability.

Simulation experiments are conducted to assess the performance of the new TOA estimation algorithm. Thereby, the comparison is done against the well-known CLEAN algorithm for a sample-by-sample based TOA estimation and against three energy detector based receiver algorithms. The obtained results highlight the effectiveness of the developed approach.

The developed TOA estimation algorithm is completely different from other techniques in the literature, and it is based on a proportionality test between two sliding frames. These latter are modeled by two AR processes. Then a distance measure is used to check whether or not the power spectral densities are proportional.