Bilinear systems offer a promising approach for nonlinear control because a broad class of nonlinear problems can be reformulated in bilinear form. In this paper system identification is shown to be a technique to obtain such a bilinear approximation of a nonlinear system. Recent discrete-time bilinear model identification methods rely on Input-Output-to-State Representations. These IOSRs are e...

Introduction:  The  advent  of  dual-modality  PET/CT  scanners  has  revolutionized  clinical  oncology  by  improving lesion localization and facilitating treatment planning for radiotherapy. In addition, the use of  CT images for CT-based attenuation correction (CTAC) decreases the overall scanning time and creates  a noise-free  attenuation  map  (6map).  CTAC  methods  include  scaling,  s...

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computati...

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

In this work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.

The bilinear Generalized predictive controller is modified to account for unmodelled plant uncertainties and bounded disturbances. First, a generalized predictive control law is derived by means of minimizing a quadratic cost function and then modified by introducing an estimate of the modeling error as a feedback. The robustness results are derived by neither requiring a prior knowledge of the...

In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...

The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics is determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and spanreachability in ter...