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This paper proposes an original interval-based method to compute an outer approximation of all invariant sets (such as limit cycles) of a continuous-time nonlinear dynamic system, which are included inside a prior set of the state space. Contrary to all other existing approaches, our method has the following properties: first, it is guaranteed (a solution cannot be lost); second, it is applicable to a large class of systems without any specific assumption such as the knowledge of a Lyapunov function or any partial linearity; and third, there is no need to integrate the system. [ABSTRACT FROM AUTHOR]

A fast simulation method for time-derivative cellular neural networks (TDCNN) is proposed. Using forward Euler approximation (FEA) for the derivative of the cell state and the backward Euler approximation (BEA) for the derivatives of the neighboring cell states enables the recursive computation of the cell state and provides a speed advantage of orders of magnitude. The state equations are then packed into a vector-matrix form which enables the previously empirically given time constraint to be expressed as a matrix condition. It is shown that using both FEA and BEA leads to a second-order difference equation whose corresponding second-order differential equation is derived and shown to yield the same simulation results. [ABSTRACT FROM PUBLISHER]

This paper presents a design-oriented analytical approach for predicting fast-scale instability in power electronics converters under voltage-mode control strategy. This approach is based on the use of the ripple amplitude of the feedback control voltage as an index for predicting subharmonic oscillations in these systems. First, the work revisits the stability analysis technique based on the nonlinear discrete-time model, demonstrating that the ripple amplitude can be included within the expression of the Jacobian matrix of this model, hence giving a mathematical support to extend the ripple index to more complex topologies. A simple but representative buck converter under voltage-mode control is used to illustrate the approach. Using the ripple-based index, closed-form expressions of stability boundaries are derived. Unlike other available results obtained from existing methods, the stability boundary, in this work is expressed analytically in terms of both power stage and controller design parameters. Moreover, one can determine how these parameters are involved in the closed form expressions and, furthermore, how each parameter affects the stability of the system. The approach is validated by numerical simulations from the state equations and also experimentally within a wide range of the design parameter space. [ABSTRACT FROM PUBLISHER]

Abstract: The unidirectional wave motions of many physical systems may all be represented by a set of state equations describing the dynamic state of certain physical variables in acoustics, mechanics, optics, and geophysics, varying in time and in one-spatial coordinate. Through the application of Fourier transforms in time variable, the state equations are reduced to a linear system of differential equations with variable coefficients, which may be analyzed by the traditional method of transfer matrix (the propagator of state variables) or the recently developed method of reverberation-ray matrix. The mathematical formulations of both matrices and applications to seemingly two unrelated physical systems, the propagation of axial and flexural waves in a multi-branched framed structure, and that of seismic waves in a layered medium, are reviewed in this article. By detailed comparisons with the method of transfer matrix and others, we conclude that the reverberation-ray analysis is a viable alternative to the solutions of initial value and two-point boundary value problems of unidirectional wave motions. [Copyright &y& Elsevier]

Abstract: Taking into account uncertainties in model parameter values is a crucial point for studying robustness in modeling and in control. This paper proposes to construct in a systematic and graphical procedure two forms of the linear state equation usually found in the literature for dealing with the robustness problem in the case of structured uncertainties on parameters. It is shown how to model uncertainties in a bond graph approach, in the case of additive or multiplicative parametric variations. [Copyright &y& Elsevier]