A class of single input single output bilinear systems described by their input–output difference equation is considered. A simple expression for the Volterra kernels of the system is derived in terms of the coefficients of difference equation. An algorithm, based on the singular value decomposition of a generalized Hankel matrix, is also developed. The algorithm is then used to find a reduced-...

This paper provides a receding horizon control method for bilinear systems in the presence input constraints. Periodically-invariant sets are derived for a bilinear system with respect to a series of time-varying state feedback gains. The dual-mode control strategy is adopted and the periodicallyinvariant sets are used as target invariant sets. The state feedback gains used to define the target...

Abstract— This paper presents the modified bilinear volterra adaptive filter technique without considering the cross correlated input and output terms for nonlinear system identification. The result obtained by our proposed technique is compared with trigonometric, power and projected wavelet series expansions. In the present implementation the identification problem is performed on four series...

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation...

L p estimates for non smooth bilinear Littlewood-Paley square functions on R. Abstract In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. Mainly we prove boundedness-properties in Lebesgue spaces for them. Let us consider the function φn satisfying c φn(ξ) = 1 [n,n+1] (ξ) and consider the bilinear operator Sn(f, g)(x) := R ...

Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so called CoifmanMeyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multiplier...

In this work, switching systems are named endogenous when their switching pattern is controllable. Linear endogenous switching systems can be considered as a particular class of bilinear control systems. The key idea is that both types of systems are equivalent to polysystems i.e. to systems whose flow is piecewise smooth. The reachable set of a linear endogenous switching system can be studied...

We present the first identity-based traitor tracing scheme. The scheme is shown to be secure in the standard model, assuming the bilinear decision Diffie-Hellman (DBDH) is hard in the asymmetric bilinear pairing setting, and that the DDH assumption holds in the group defining the first coordinate of the asymmetric pairing. Our traitor tracing system allows adaptive pirates to be traced. The sch...

This paper proposes a trajectory planning and tracking approach for bilinear systems that approximate weakly nonlinear systems, based on orthogonal functions and especially the use of operational integration and product matrices. These operational tools allow the conversion of a bilinear differential state equation into an algebraic one depending on initial and final conditions. Arranging and s...

At Eurocrypt 2010, Freeman proposed a transformation from pairing-based schemes in composite-order bilinear groups to equivalent ones in prime-order bilinear groups. His transformation can be applied to pairing-based cryptosystems exploiting only one of two properties of composite-order bilinear groups: cancelling and projecting. At Asiacrypt 2010, Meiklejohn, Shacham, and Freeman showed that p...