2D systems feedback compensation: an approach based on commutative linear transformations

AbstractAlgebraic properties of a pair of commutative matrices associated with an ideal in R[z1, z2] are exploited for characterizing the closed loop polynomial variety of a 2D system. Also algorithms are given to find under what constraints the closed loop variety can be assigned and to compute the MFD of a compensator

On the Connection Between the Stability of Multidimensional Positive Systems and the Stability of Switched Positive Systems

In this work, we study the connection of the stability of multidimensional positive systems with the stability of switched positive systems. In a previous work, we showed that the stability of a multidimensional positive system implies the stability of a related switched positive system. Here, we investigate the reciprocal implication

Burst Erasure Correction of 2D convolutional codes

In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. In particular, we present a procedure to recover bursts of erasures that are distributed in a diagonal line. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main result reduces the decoding problem of 2D convolutional codes to a problem of decoding a set of associated 1D convolutional codes

NuSTAR discovery of a cyclotron line in the accreting X-ray pulsar IGR J16393-4643

The high-mass X-ray binary and accreting X-ray pulsar IGR J16393-4643 was observed by NuSTAR in the 3-79 keV energy band for a net exposure time of 50 ks. We present the results of this observation which enabled the discovery of a cyclotron resonant scattering feature with a centroid energy of 29.3(+1.1/-1.3) keV. This allowed us to measure the magnetic field strength of the neutron star for the first time: B = (2.5+/-0.1)e12 G. The known pulsation period is now observed at 904.0+/-0.1 s. Since 2006, the neutron star has undergone a long-term spin-up trend at a rate of P' = -2e-8 s/s (-0.6 s per year, or a frequency derivative of nu' = 3e-14 Hz/s ). In the power density spectrum, a break appears at the pulse frequency which separates the zero slope at low frequency from the steeper slope at high frequency. This addition of angular momentum to the neutron star could be due to the accretion of a quasi-spherical wind, or it could be caused by the transient appearance of a prograde accretion disk that is nearly in corotation with the neutron star whose magnetospheric radius is around 2e8 cm.Comment: Accepted for publication in the Astrophysical Journal, 7 pages, 8 figures, 2 table

Input-state-output representations and constructions of finite-support 2D convolutional codes

Two-dimensional convolutional codes are considered, with codewords having compact support indexed in N^2 and taking values in F^n, where F is a finite field. Input-state-output representations of these codes are introduced and several aspects of such representations are discussed. Constructive procedures of such codes with a designed distance are also presented. © 2010 AIMS-SDU

Composition codes

In this paper we introduce a special class of 2D convolutional codes, called composition codes, which admit encoders G(d1,d2) that can be decomposed as the product of two 1D encoders, i.e., G(d1,d2)=G2(d2)G1(d1). Taking into account this decomposition, we obtain syndrome formers of the code directly from G1(d1) andG2(d2), in case G1(d1) andG2(d2) are right prime. Moreover we consider 2D state-space realizations by means of a separable Roesser model of the encoders and syndrome formers of a composition code and we investigate the minimality of such realizations. In particular, we obtain minimal realizations for composition codes which admit an encoder G(d1,d2)=G2(d2)G1(d1) withG2(d2) a systematic 1D encoder. Finally, we investigate the minimality of 2D separable Roesser state-space realizations for syndrome formers of these codes.publishe