Model reduction with a priori relative/multiplicative error bounds in L 1 norm is studied. Inverse-weighted balanced truncation (IWBT) is proposed that is a variant of the Enns' algorithm 8]. It is shown that IWBT is equivalent to the balanced stochastic truncation (BST). This equivalence leads to the extension of an improved relative/multiplicative error bound for BST obtained by Wang and Safo...

This paper considers the problem of direction-of-arrival (DOA) estimation of coherent signals on passive coprime arrays, where we resort to the fourth-order cumulants of the received signal to explore more information. A fourth-order cumulant matrix (FCM) is introduced for the coprime array. The special structure of the FCM is combined with the array configuration to resolve the coherent signal...

The model/data consistency problem for coprime factorizations considered here is this: Given some possibly noisy frequency-response data obtained by running open-loop experiments on a system, show that these data are consistent with a given family of perturbed coprime factor models and a timedomain L1 noise model. In the noise-free open-loop case, the model/data consistency problem boils down t...

Let S be a finite set of positive integers. A “coprime base for S” means a set P of positive integers such that (1) each element of P is coprime to every other element of P and (2) each element of S is a product of powers of elements of P. There is a natural coprime base for S. This paper introduces an algorithm that computes the natural coprime base for S in essentially linear time. The best p...

Within a lattice approach, the purpose of this paper is to give general necessary and sufficient conditions for internal stabilizability and for the existence of (weakly) left-/right-/doubly coprime factorizations of multi input multi output linear systems. These results extend the ones recently obtained in [24] for single input single output systems. In particular, combining these results with...

We consider the efficient solution of a class of coprime factorization based controller approximation problems by using frequency-weighted balancing related model reduction approaches. It is shown that for some special stability enforcing frequency-weights, the computation of the frequency-weighted controllability and observability grammians can be done by solving reduced order Lyapunov equatio...