Time-frequency representations transform a one-dimensional function into a two-dimensional function in the phase-space of time and frequency. The transformation to accomplish is a nonlinear transformation and there are an infinite number of such transformations. We obtain the governing differential equation for any two-dimensional bilinear phase-space function for the case when the governing eq...

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a timedelay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time...

The Groth-Sahai proof system (EUROCRYPT 2008, SIAM Journal of Computing 41(5) [GS12]) provides e cient non-interactive witness-indistinguishable (NIWI) and zero-knowledge (NIZK) proof systems for languages over bilinear groups and is a widely-used versatile tool to design e cient cryptographic schemes and protocols. We revisit randomization of the prover in the GS proof system. We nd an unnotic...

Original scientific paper A zero-sum game approach for H∞ robust control of continuous-time singularly perturbed bilinear quadratic systems with an additive disturbance input is presented. By regarding the stochastic disturbance (or the uncertainty) as "the nature player", the H∞ robust control problem is transformed into a twoperson zero-sum dynamic game model. By utilizing the singular pertur...

In CRYPTO 2012, Sahai et al. raised the concern that in a cloud control system revocation of past keys should also be accompanied by updation of previously generated ciphertexts in order to prevent unread ciphertexts from being read by revoked users. Self-updatable encryption (SUE), introduced by Lee et al. in ASIACRYPT 2013, is a newly developed cryptographic primitive that realizes ciphertext...

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...

In this work, we prove the uniform regularity of smooth solutions to full compressible MHD system in \(\mathbb{T}^3\). Here our result is obtained by using bilinear commutator and product estimates.

Many problems in kinematic synthesis of mechanisms and robots lead naturally to systems of bilinear equations in design parameters. Such systems are typically solved using well-known methods for solutions of systems of polynomial equations, e.g., Dialytic Elimination, Grobner bases, and Polynomial Continuation. This paper presents a new nullspace analysis method for solving a system of bilinear...

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem real-world industrial applications. Koopman operator theory allows one to analyze through the lens of linear bilinear systems. The key idea these methods lies in transformation coordinates system into observables, which are that allow representation original (control system) as highe...

In this paper, a ‘four-block’ subspace system identification method for combined deterministic-stochastic bilinear systems is developed. Estimation of state sequences, followed by estimation of system matrices, is the central component of subspace identification methods. The prominent difference of our new approach is a ‘four-block’ arrangement of data matrices which leads to a linearization of...