This note describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. Wh...

Absfract-This paper shows that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result, a Lyapunovtheoretic definition is proposed for bounded ...

To obtain coprime polynomial pairs, it is often used an approach that consists of taking two random polynomials of the required degrees and testing whether they are relatively prime. If they are not, they are discarded and another pair is tried. The test can obviously be carried out very efficiently. Although in many cases the probability of success for the test is close to 1, this test approac...

Coprime arrays enable Direction-of-Arrival (DoA) estimation of an increased number sources. To that end, the receiver estimates autocorrelation matrix a larger virtual uniform linear array (coarray), by applying selection or averaging to physical array's estimates, followed spatial-smoothing. Both and have been designed under no optimality criterion attain arbitrary (suboptimal) Mean-Squared-Er...

where the polynomial matrices Ni(s) and D(s) form a normal external description (NED) of (C, A H ) ; see [11]. The matrices N(s) := CNx(s) and D(s) then form, not necessarily coprime, a matrix fraction description (MFD) of (C,A,B). Recall that Ni(s) and D(s) are right coprime with D(s) being column reduced. The column degrees, Cj := degciD(s), i = 1,2,... ,m, are the controllability indices of ...

The open problem of the existence of double coprime factorizations (DCFs) for multi-input/multi-output (MIMO) multidimensional (nD) linear systems is considered in this paper. It is shown that DCFs exist for a class of MIMO nD linear systems. A simple and efficient method is proposed for the construction of DCFs. The main result of the paper is to show how to construct a coprime (over the ring ...

Abstract We improve on a result by Svetlana Jitomirskaya and Wencai Liu dealing with inhomogeneous Diophantine approximation in the coprime setting.