A factorization approach to the analysis of asynchronous interconnected discrete-time systems with arbitrary clock ratios

This work presents a model for distributed feedback systems that operate at almost identical sampling rates. A Toeplitz model approach is used in order to capture the effect of small synchronization errors. In previous works, a similar model was used to formulate necessary and sufficient stability conditions, under the simplifying assumption that the frequency ratios of the subsystems involved have a special rational form. In this sequel this assumption is lifted, by proposing a factorization of the feedback matrix that holds for arbitrary clock frequency ratios. This factorization property constitutes the first necessary step towards the generalization of the previous stability results to the general case of arbitrary clock frequency ratios. Furthermore, this generalization may enable the derivation of simple stability and robustness criteria in the presence of time-varying uncertain synchronization errors. This work presents a model for distributed feedback systems that operate at almost identical sampling rates. A Toeplitz model approach is used in order to capture the effect of small synchronization errors. In previous works, a similar model was used to formulate necessary and sufficient stability conditions, under the simplifying assumption that the frequency ratios of the subsystems involved have a special rational form. In this sequel this assumption is lifted, by proposing a factorization of the feedback matrix that holds for arbitrary clock frequency ratios. This factorization property constitutes the first necessary step towards the generalization of the previous stability results to the general case of arbitrary clock frequency ratios. Furthermore, this generalization may enable the derivation of simple stability and robustness criteria in the presence of time-varying uncertain synchronization errors.