This paper considers the identi cation of time-invariant bilinear models using observed input{output data. Bilinear models represent a parsimonious class of nonlinear parameterisations and have been used in a variety of applications. However the performance of the bilinear model can be limited in practice when standard least-squares techniques are used, as this leads to biased parameter estimat...

Many nonlinear plants can be better approximated and controlled using bilinear models instead of linear ones. For many bilinear models, a feedback linearization can be achieved, forcing the plant to behave like a linear system, with all known advantages. In practical applications, however, this means that the dynamic range of the applied control input is enlarged, increasing the danger of runni...

Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of large-scale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bi-linearization method, which extends Krylov subspace techniques for linear systems. In this approach, the nonlinear system is first approxim...

In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods where interpolation is forced on some of the leading subsystem transfer functions, the new framework shows how to enforce multipoint interpolation of the un...

This paper formulates a bilinear observer for a bilinear state-space model. Relationship between the bilinear observer gains and the interaction matrices are established and used in the design of such observer gains from input-output data. In the absence of noise, the question of whether a deadbeat bilinear observer exists that would cause the state estimation error to converge to zero identica...

A well known method to transfer the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with angular frequency equal to the difference of the eigenvalues. This paper gives a theoretical proof of this experimental result. We introduce a notion of efficiency and demonstrate its interest for the design of controls on the example of ...

We construct two efficient Identity Based Encryption (IBE) systems that are selective identity secure without the random oracle model in groups equipped with a bilinear map. Selective identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead of time to the identity that it intends to attack, whereas in the sta...

In this paper, we will discuss the problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known H2norm for linear systems. We revisit existing first order necessary conditions for H2-optimality based on the solutions of generalized Lyapunov equations arising in bilinear system theory and present an iterative algorithm which, upon conv...

This paper investigates both the H∞ and robust H∞ reduced order unbiased filtering problems for respectively a nominal bilinear system and a bilinear system affected by norm-bounded structured uncertainties in all the system matrices. First, an algebraic framework is used to solve the unbiasedness condition and second, a change of variable is introduced on the inputs of the system to reduce the...