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Abstract: In this paper, the problem of H ∞ filtering for neutral systems with mixed time-varying delays and nonlinear perturbations is investigated. Some new delay-dependent sufficient conditions are presented to ensure that the filtering error system is asymptotically stable with a prescribed level of H ∞ noise attenuation. In addition, the design procedures for the existence of such filter are presented in terms of a set of linear matrix inequalities (LMIs). Slack variables and convex combination technique are adopted to reduce the conservatism of obtained results. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of robust fault detection filter (RFDF) design for a class of linear systems with some nonlinear perturbations and mixed neutral and discrete time-varying delays is investigated. By using a descriptor technique, Lyapunov–Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Based on the Luenberger type observers, the explicit expression of the filters is derived for the fault such that both asymptotic stability and a prescribed level of disturbance attenuation are satisfied for all admissible nonlinear perturbations. A numerical example is provided to demonstrate the effectiveness and the applicability of the proposed method. [Copyright &y& Elsevier]

• Nonlinear corrections are used in the canonical quantization of a weakly nonideal Bose gas at zero temperature. • Additional nonoscillation modes recover the canonical commutation relations at the linear order and at the next order. • Consideration of nonlinear corrections automatically solves the problem of nonconserved particle number. In the present paper, quantization of a weakly nonideal Bose gas at zero temperature along the lines of the well-known Bogolyubov approach is performed. The analysis presented in this paper is based, in addition to the steps of the original Bogolyubov approach, on the use of nonoscillation modes (which are also solutions of the linearized Heisenberg equation) for recovering the canonical commutation relations in the linear approximation, as well as on the calculation of the first nonlinear correction to the solution of the linearized Heisenberg equation which satisfies the canonical commutation relations at the next order. It is shown that, at least in the case of free quasi-particles, consideration of the nonlinear correction automatically solves the problem of nonconserved particle number, which is inherent to the original approach. [ABSTRACT FROM AUTHOR]

• Nonlinear equation of motion for a perturbation is necessary to obtain correct values of the integrals of motion of the perturbation. • Nonlinear equation of motion also ensures the conservation over time of the integrals of motion of the perturbation. • The additivity property is valid for the integrals of motion of properly defined nonlinear modes forming the whole perturbation. In this paper, classical small perturbations against a stationary solution of the nonlinear Schrödinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over time) nonzero expressions for the basic integrals of motion of a perturbation even in the quadratic order in the expansion parameter, it is necessary to consider nonlinear equations of motion for the perturbations. It is also shown that, despite the nonlinearity of the perturbations, the additivity property is valid for the integrals of motion of different nonlinear modes forming the perturbation (at least up to the second order in the expansion parameter). [ABSTRACT FROM AUTHOR]