Semistate models of electrical circuits including memristors

In this paper we present several semistate or differential‐algebraic models arising in nodal analysis of nonlinear circuits including memristors. The goal is to characterize the tractability index of these models under strict passivity assumptions, a key issue for the numerical simulation of circuit dynamics. We show that the main model, which combines memristors' fluxes and charges, is index two. From a technical point of view, this result is based on the use of a projector along the image of the leading matrix, in contrast to previous index analyses. For charge‐controlled memristors, the elimination of fluxes yields an index one system in topologically nondegenerate circuits, and an index two model otherwise. Analogous results are also proved to hold for flux‐controlled memristors. Our framework accommodates coupling effects among resistors, memristors, capacitors and inductors. Copyright © 2010 John Wiley & Sons, Ltd.     

非线性电路平衡点全局渐近稳定的充分必要条件

利用向量比较原理,得到了确定非线性电路平衡点全局渐近稳定的充分必要条件。结果表明,非线性非自治电路的唯一稳态的充分必要条件,可以用一个常数矩阵的Hurwitz条件决定。     

A note on stability of linear time‐variant electrical circuits having constant eigenvalues

The main aspect of this paper is to show that the stability of linear time‐variant systems cannot be estimated from the location of the eigenvalues. For this purpose, two simple time‐variant electrical circuits are presented, which have constant eigenvalues. As will be shown, the time‐variant circuits can be asymptotically stable although there is a positive eigenvalue and this circuit can be unstable despite negative eigenvalues only. The idea behind is a suited time‐variant state transformation of a linear time‐invariant system. An electrical interpretation of both systems and of state transformations allows for an energetic evaluation from an electrical point of view even though the analytical solution is not necessarily known. Copyright © 2012 John Wiley & Sons, Ltd.     

A matrix pencil approach to the local stability analysis of non‐linear circuits

This paper addresses local stability issues in non‐linear circuits via matrix pencil theory. The limitations of the state–space approach in circuit modelling have led to semistate formulations, currently framed within the context of differential‐algebraic equations (DAEs). Stability results for these DAE models can be stated in terms of matrix pencils, avoiding the need for state–space reductions which are not advisable in actual circuit simulation problems. The stability results here presented are applied to electrical circuits containing non‐linear devices such as Josephson junctions or MOS transistors. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive variable universe of discourse fuzzy control for a class of nonlinear systems with unknown dead zones

In this paper, based on an adaptive nonbackstepping design algorithm, we proposed a novel variable universe of discourse fuzzy control (VUDFC) approach for a class of single‐input–single‐output strict‐feedback nonlinear systems with unknown dead‐zone inputs. Firstly, we convert the form of system into a normal form on the basis of some new state variables and coordinate transformation; at the same time, state‐feedback control is changed to output‐feedback control. Secondly, we design observers to estimate the new unmeasurable states. Then, different from considering the traditional backstepping‐based fuzzy control scheme, we introduce a direct VUDFC scheme, which is mainly based on changing of contraction‐expansion factors to modify the universe of discourse online, and fuzzy rules can automatically reproduce to develop the control performance; thus, the size of initial rule base is greatly reduced. This new algorithm can alleviate tracking error, improve the accuracy of the system, and strengthen robustness. Lastly, according to Lyapunov theorem analysis, we prove that all the signals in the closed‐loop system can be guaranteed to be stable, and the output can track the reference signal very well. Simulation results illustrated the effectiveness of the proposed VUDFC approach.     

A closed‐form equation approach to multi‐port/multi‐zone behavioral modeling of GaN FET Amplifiers

In this paper, a systematic method for the simulation of weakly and mildly nonlinear GaN FET amplifiers is reported. The core of the proposal is a third‐order Volterra‐based behavioral model with multi‐spectral and multi‐node capabilities that is formally derived from a circuit‐level representation. Starting with the equivalent circuit of a typical FET device with thermal power feedback and fading memory, described in terms of its large‐signal functions, closed‐form expressions for the kernels at the gate, drain and thermal nodes are developed up to the third order. The use of these kernels allows the calculation of the responses in the dc, first‐, second‐ and third‐harmonic zones, which are shown to be dependent on the frequency response of the amplifier circuit terminating impedances and thermal filter. The simulation approach has been applied to calculate the nonlinear response of a typical power amplifier circuit, showing the ability of the proposed approach to provide an accurate prediction of multi‐spectral, multi‐node, multi‐bias characteristics, including AM/AM‐AM/PM conversion, spectral regrowth, intermodulation, and temperature rise, under diverse input signal waveforms and bandwidths. These results have been successfully compared with commercial CAD tools based on harmonic balance or envelope simulation. Copyright © 2014 John Wiley & Sons, Ltd.