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Inhomogeneous linear ordinary differential equations (ODEs) and systems of ODEs can be solved in a variety of ways. However, hardware circuits that can perform the efficient analog computation to solve them are rarely in the literature. To address such problems, this paper proposes a general method of using a memristor-capacitor (M-C) circuit to solve inhomogeneous linear ODEs and systems of ODEs of any order in initial value problems. The M-C circuit can match the coefficients of the equations sought by adjusting the memristor resistance value according to the coefficient formula proposed in the paper, which has higher programmability. Then, some ODEs and systems of ODEs are given in the paper as examples to evaluate the proposed method. According to the comparison results based on MATLAB software simulation and the simulation based on OrCAD software, the designed M-C circuit has an effective improvement in speed and the accuracy exceeds 99.95% in software simulation. Based on practical verification, this paper gives the actual M-C circuit experiment based on PCB. Moreover, the proposed method can be used to quickly solve the object motion state in the spring mass damping system in actual engineering, and the accuracy can reach 99.98%. [ABSTRACT FROM AUTHOR]

This paper addresses and experimentally demonstrates a programmable linear equation solver by analog computation. A set of differential equations using transconductance devices directly translated from circuit theory converges to the linear equation solution. These energy-efficient analog techniques are experimentally demonstrated in a configurable analog platform. The resulting analog linear equation solution circuits are effectively analog filters. The paper analyzes the algorithmic issues and analog numerical analysis issues, including accuracy, convergence time, and the interpretation of condition number for analog solutions. [ABSTRACT FROM AUTHOR]

In this paper, based on sampled-data control method, we address the stabilization problem for a general class of linear continuous-time fractional systems whose solution contains the Mittag-Leffler function that does not obey the basic exponentiation identity. By considering the infinite memory and hereditary characteristics of fractional-order calculus, we propose a sampled-data controller that guarantees the resulting closed-loop system to be asymptotically stable. Simulation examples are presented to demonstrate the effectiveness of the proposed controller and verify the established results. [ABSTRACT FROM AUTHOR]

This paper focuses on the small-signal stability analysis of systems modelled as differential-algebraic equations and with inclusions of delays in both differential equations and algebraic constraints. The paper considers the general case for which the characteristic equation of the system is a series of infinite terms corresponding to an infinite number of delays. The expression of such a series and the conditions for its convergence are first derived analytically. Then, the effect on small-signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on hybrid control systems recast into delay algebraic-differential equations as well as a benchmark dynamic power system model with inclusion of long transmission lines. [ABSTRACT FROM AUTHOR]

Efficient simulation of switched-mode power conversion circuits is necessary for the analysis and optimization of power electronics. This paper introduces the extended impedance method (EIM) to the simulation and analysis of general switched-mode power converter circuits. By using the EIM method, the conventional impedance concept can be extended to involve more linear time-variant (LTV) and nonlinear devices, such as MOSFET switches and diodes, which are commonly used in switched-mode power conversion circuits. EIM models a circuit network from the component level in the frequency domain, rather than from the system-level constitutive differential equation in the time domain. Compared with the conventional averaging method, EIM can reveal more high-frequency features of a switched-mode converter circuit, in particular, those around the switching instants. A buck converter is taken as a representative example to validate the EIM based analysis. Both the simulation and experimental results prove that EIM provides precise numerical results, which match the real waveform, as the commercial simulators, e.g. PSpice and ADS, do. Moreover, it largely reduces the computational complexity towards more efficient and more flexible steady-state analysis of switched-mode power electronics. [ABSTRACT FROM AUTHOR]

Design details and analysis of the properties of a hysteresis switching controller for the Ćuk converter are provided in this paper. The design is based on a switching control law which minimizes a common Lyapunov function derivative for the converter's continuous modes of operation. These continuous modes of operation are both marginally stable which causes some particularities in the design procedure. The design also meets the specifications in terms of the converter's duty ratio and the frequency limitations. The proposed hysteresis controller performance is analyzed with respect to the operating modes of the converter and illustrated with a number of representative and relevant simulations. [ABSTRACT FROM PUBLISHER]

As is known to all that the Lyapunov-Krasovskii functional (LKF) has played a vital role in studying the fixed-time (FXT) stability of the time-delayed Filippov discontinuous systems. When investigating the FXT stability of the time-delayed discontinuous systems, the interesting topic is to provide the more relaxed conditions imposed on the LKF and obtain the more accurate settling-time (ST). This paper aims to investigate the new FXT stability lemma with more relaxed conditions for the time-delayed Filippov discontinuous systems. By using some novel inequality techniques and analytical methods, the new FXT stability lemma is established and more accurate ST is estimated. The traditional discussion about $0 < V < 1$ and $V \geq 1$ is not required. For the purpose of validation, FXT stabilization of discontinuous inertial networks with mixed time delays is considered. By using differential inclusions theory and the new FXT stability lemma, the delay-dependent FXT stabilization criteria are derived. It is the first time to derive the delay-dependent FXT stabilization criteria for the discontinuous inertial networks. Finally, examples are given to show the effectiveness of the established results. [ABSTRACT FROM AUTHOR]

This paper develops a neural network for solving the general nonsmooth convex optimization problems. The proposed neural network is modeled by a differential inclusion. Compared with the existing neural networks for solving nonsmooth convex optimization problems, this neural network has a wider domain for implementation. Under a suitable assumption on the constraint set, it is proved that for a given nonsmooth convex optimization problem and sufficiently large penalty parameters, any trajectory of the neural network can reach the feasible region in finite time and stays there thereafter. Moreover, we can prove that the trajectory of the neural network constructed by a differential inclusion and with arbitrarily given initial value, converges to the set consisting of the equilibrium points of the neural network, whose elements are all the optimal solutions of the primal constrained optimization problem. In particular, we give the condition that the equilibrium point set of the neural network coincides with the optimal solution set of the primal constrained optimization problem and the condition ensuring convergence to the optimal solution set in finite time. Furthermore, illustrative examples show the correctness of the results in this paper, and the good performance of the proposed neural network. [ABSTRACT FROM AUTHOR]

This paper introduces new fundamentals of the three-dimensional \nabla\times n RLC circuit network in the fractional-order domain. First, we derive the general formula of the typical equivalent impedance of the circuit network in different cases by using matrix transform method and the difference equation model. Then, we systematically investigate the effects of the five system parameters (inductance (L), capacitance (C), the number of circuit units (n), and fractional orders \alpha and \beta) on the impendence characteristics and the phase characteristics of two different cases. Specifically, interesting phenomena and laws are presented by the numerical simulations. Moreover, a comparative analysis about the impendence characteristics and the phase characteristics of the two cases for the fractional-order three-dimensional circuit network is studied in detail. Finally, the results of PSpice simulation are presented to validate the study. [ABSTRACT FROM AUTHOR]

A Lyapunov approach to the characterization of forced vibration for continuous-time systems was recently proposed in [12]. The objective of this paper is to derive counterpart results for discrete-time systems. The class of oscillatory input signals to be considered include sinusoidal signals, multitone signals, and periodic signals which can be described as the output of an autonomous system. The Lyapunov approach is developed for linear systems, homogeneous systems (difference inclusions), and nonlinear systems (difference inclusions), respectively. It is established that the steady-state gain can be arbitrarily closely characterized with Lyapunov functions if the output response converges exponentially to the steady state. We also evaluate other output measures such as the peak of the transient response and the convergence rate. Applying the results to linear difference inclusions, optimization problems with linear matrix inequality constraints can be formulated for the purpose of estimating the output measures. This paper's results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals. Similar to continuous-time systems, it is observed that the peak of the frequency response can be strictly larger than the L2 gain for a linear difference inclusion. [ABSTRACT FROM AUTHOR]

In this paper, a new efficient circuit level analysis is introduced considering the effect of all harmonics and multi-injection for locking and pulling phenomena in $N$ -stage differential and single-ended ring oscillators with the $RC$ -load. Analytical equations are derived for the locking range in both single- and multi-injection cases. At the beginning, using a nonlinear approach, the voltage amplitude and frequency of $RC$ -load free running ring oscillators are derived as simple closed-form equations. Then, to analyze the mentioned phenomena, differential equations describing the circuit behavior are derived by circuit level equations. Furthermore, analyses are extended for general multi-injections with arbitrary amplitude and excess phase for different output nodes. The simplest and most accurate analytical equation is achieved for the locking range. In contrary to few previous works, the proposed analysis is derived directly from equations governing ring oscillators so that we can expect results with more accuracy without any tedious and time-consuming pre-processing like perturbation projection vector. To evaluate the analysis, many simulations have been performed. Simulation results validate presented analytical equations, which provide useful design insights. Absolute percent error of all proposed equations in comparison with simulation results is better than 20%. [ABSTRACT FROM PUBLISHER]

In this paper, a general structure of linear-phase finite impulse response filters, whose frequency responses satisfy given derivative constraints imposed upon an arbitrary frequency, is proposed. It is comprised of a linear combination of parallelly connected subfilters, called the cardinal filters, with weighted coefficients being the successive derivatives of the desired frequency response at the constrained frequency. An advantage of such a cardinal filters design is that only the weighted coefficients are relevant to the desired frequency response but not the cardinal filters; hence, a dynamic adjustment of the filter system becomes feasible. The key to derive the coefficients of cardinal filters is the determination of the power series expansion of certain trigonometric-related functions. By showing the elaborately chosen trigonometric-related functions satisfy specific differential equations, recursive formulas for the coefficients of cardinal filters are subsequently established, which make efficient their computations. At last, a simple enhancement of the cardinal filters design by incorporating the mean square error minimization is presented through examples. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear state-space model (SSM) for a low power 28-nm complementary metal–oxide–semiconductor switched-capacitor digital-to-analog converter. The proposed model utilizes current–voltage (I-V) input and output relationships for passive devices, which are described by a set of first-order differential equations. The proposed model significantly increases accuracy when compared with the state-of-the-art models. The SSM simulation results have been verified using SpectreRF transistor-level simulations and validated by on-chip measurements. [ABSTRACT FROM AUTHOR]

In this paper, we propose a neural network modeled by a differential inclusion to solve a class of nonsmooth convex optimization problems, where the constraints are defined by a class of nonsmooth convex inequality constraints and a class of affine equality constraints. For any initial point, the solution of the proposed network is global existent, unique and uniformly bounded, which is just the “slow solution” of network. By the regularization item, without any estimation on the exact penalty parameters, the solution of proposed network is convergent to the optimal solution set of optimization problem. Moreover, when the feasible region satisfies another condition, the solution of proposed network converges to the feasible region in finite time and to the particular element in the optimal solution set with the smallest norm, which indicates that our proposed neural network is globally attractive. Some numerical examples are presented to illustrate the effectiveness of the proposed neural network for solving nonsmooth convex optimization problems. [ABSTRACT FROM AUTHOR]

The object of this paper is to give a complete treatment of the realizability of positive-real biquadratic impedance functions by six-element series-parallel networks comprising resistors, capacitors, and inductors. This question was studied but not fully resolved in the classical electrical circuit literature. Renewed interest in this question arises in the synthesis of passive mechanical impedances. Recent work by the authors has introduced the concept of a regular positive-real functions. It was shown that five-element networks are capable of realizing all regular and some (but not all) nonregular biquadratic positive-real functions. Accordingly, the focus of this paper is on the realizability of nonregular biquadratics. It will be shown that the only six-element series-parallel networks which are capable of realizing nonregular biquadratic impedances are those with three reactive elements or four reactive elements. We identify a set of networks that can realize all the nonregular biquadratic functions for each of the two cases. The realizability conditions for the networks are expressed in terms of a canonical form for biquadratics. The nonregular realizable region for each of the networks is explicitly characterized. [ABSTRACT FROM PUBLISHER]

The analysis of complicated circuits containing nonlinear electrical elements is commonly performed via numerical algorithms of simulation programs. However, an analytical solution can be preferable to the numerical approach, particularly for the needs of basic research. This paper introduces a methodology of the analytical solution of voltage/current response of the memristor to its excitation from ideal current/voltage source, with the memristor being characterized by the memristance-charge or memductance-flux relationships. The procedure is explained on examples of a TiO2 memristor with linear dopant drift and of a hydraulic memristor. [ABSTRACT FROM PUBLISHER]

Switched dynamical systems can be found in many practical electronic circuits, such as various kinds of power converters, chaos generators, etc. This paper is concerned with the filter design problem for a class of switched system with average dwell time switching. Mode-dependent full-order filters are designed taking a more practical phenomenon, the asynchronous switching into account, where “asynchronous” means that the switching of the filters to be designed has a lag to the switching of the system modes. New results on the stability and l2-gain analyses for the systems are first given where the Lyapunov-like functions during the running time of subsystems are allowed to increase. In light of the proposed Lyapunov-like functions, the desired mode-dependent filters can be designed in that the unmatched filters are allowed to perform in the interval of the asynchronous switching before the matched ones are applied. In H\infty sense, the problem of asynchronous filtering for the underlying systems in linear cases is formulated and the conditions of the existence of admissible asynchronous filters are obtained. Two examples are provided to show the potential of the developed results. [ABSTRACT FROM PUBLISHER]

This paper considers a class of nonsymmetric cooperative neural networks (NNs) where the neurons are fully interconnected and the neuron activations are modeled by piecewise linear (PL) functions. The solution semiflow generated by cooperative PLNNs is monotone but, due to the horizontal segments in the neuron activations, is not eventually strongly monotone (ESM). The main result in this paper is that it is possible to prove a peculiar form of the Limit Set Dichotomy for this class of cooperative PLNNs. Such a form is slightly weaker than the standard form valid for ESM semiflows, but this notwithstanding it permits to establish a result on convergence analogous to that valid for ESM semiflows. Namely, for almost every choice of the initial conditions, each solution of a fully interconnected cooperative PLNN converges toward an equilibrium point, depending on the initial conditions, as t \to +\infty. From a methodological viewpoint, this paper extends some basic techniques and tools valid for ESM semiflows, in order that they can be applied to the monotone semiflows generated by the considered class of cooperative PLNNs. [ABSTRACT FROM PUBLISHER]

In this paper, a procedure for the analysis and design of nonlinear circuits based on the Carleman linearization is presented. Since this procedure starts with the general network equations which are derived by Kirchhoff’s law, it can be used for a variety of circuits. The proposed procedure is applied for oscillator and RF mixer circuits which are a crucial part of every wireless communication system. Based on the general network equations, a transformation into equivalent polynomial differential equations is performed using the not widely known method of Kerner. This polynomial differential equation is further transformed into an equivalent infinite-dimensional system of linear differential equations. Since the infinite-dimensional linear system cannot be solved in general, an approximation by a finite one is performed using a self-consistent technique. The obtained finite linear system is used for the approximation of the infinite-dimensional linear system on a predefined interval. The approximation is utilized for the design and analysis process of the circuit, which is a challenging problem until now. [ABSTRACT FROM AUTHOR]

This paper develops a Lyapunov approach for studying convergence and stability of a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs describe the dynamics of a general system evolving in a compact convex subset of the state space. In particular, they include the dynamics of the full-range (FR) model of cellular neural networks (CNNs), which is characterized by hard-limiter nonlinearities with vertical segments in the i-v characteristic. The approach is based on the following two main tools: 1) a set-valued derivative, which enables to compute the evolution of a Lyapunov function along the solutions of the DVIs without involving integrations, and 2) an extended version of LaSalle's invariance principle, which permits to study the limiting behavior of the solutions with respect to the invariant sets of the DVIs. Then, this paper establishes conditions for convergence (complete stability) of DVIs in the presence of multiple equilibrium points (EPs), global asymptotic stability (GAS), and global exponential stability (GES) of the unique EP. These conditions are applied to investigate convergence, GAS, and GES for FR-CNNs and some extended classes of FR-CNNs. It is shown that, by means of the techniques developed in this paper, the analysis of convergence and stability of FR-CNNs is no more difficult than that of the standard (S)-CNN5. In addition, there are significant cases, such as the symmetric FR-CNNs and the nonsymmetric FR-CNNs with a Lyapunov diagonally stable matrix, where the proof of convergence or global stability is much simpler than that of the S-CNNs. [ABSTRACT FROM AUTHOR]

In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general p-th moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive scheme for the stabilization and synchronization of chaotic Lur'e systems with time-varying delay. Based on the invariant principle of functional differential equations, the strength of the feedback controller is enhanced adaptively to stabilize and synchronize chaotic Lur'e systems. The derivative-constraint that the time-varying delay is required to be differentiable and its derivation is less than one can be removed by using LaSalle-Razumikhin-type theorems. The time-varying delay is allowed to be bounded without any additional constraint or unbounded with derivative-constraint. This method is analytical, rigorous and simple to implement in practice. In addition, it is quite robust against the effect of parameters uncertainty and noise. Two examples are provided to show the effectiveness of the proposed scheme. The results of the paper demonstrate the fruitfulness of the modern feedback and adaptive control theory application to the stabilization and synchronization problems for delayed chaotic systems. [ABSTRACT FROM AUTHOR]

The paper treats an inverse problem posed in the time domain for a circuit described by a stiff system of ordinary differential equations (ODEs). Identification of model parameters (circuit elements) is performed by processing transient characteristics measured in the circuit. An illustrative example discussed throughout the paper shows that reducing the identification problem to curve fitting, which is the most general way, may be hardly used for a stiff model due to a ravine shape of the objective functional. Moreover, a necessity of solving the stiff ODE system to get a functional value makes the inverse problem be practically unsolvable. It has been shown that the initial inverse problem may be simplified significantly by taking into account linear relations which are observed between the experimental characteristics measured for a stiff system. The relation coefficients are discussed in the paper with regard to the accuracy of the approximation. Finally the initial identification problem has been reduced to a nonlinear system of algebraic equations which may be easily solved considering different sensitivity of the relation coefficients to the model parameters. The final solution is presented for different levels of "measurement" error involved in the simulation. [ABSTRACT FROM AUTHOR]

In this paper, a new Lyapunov functional-based method is proposed for the stability analysis of delayed cellular neural networks (DCNN). Global exponential stability conditions are obtained for the general DCNN, the Hopfield neural networks (]INNs), and delayed HNNs with monotonic nondecreasing and nonconstant activation functions. [ABSTRACT FROM AUTHOR]

This paper presents a new theory that addresses the issue of passivity in macromodels of electrical interconnects constructed based on the method of characteristics (MoC). The proposed approach develops a new algebraic test to check for passivity in macromodels generated using MoC. The theory behind the developed test is based on deriving the necessary and sufficient conditions for the loss of positive-realness in the admittance matrix of the developed macromodel. An algorithmic procedure is proposed to verify passivity of general macromodels derived from the MoC. The results presented in this paper can be employed to test for positive-realness in dynamical systems described by algebraic delay-differential equations with discrete commensurate delays. [ABSTRACT FROM AUTHOR]

In this paper, the linear quadratic Nash games for infinite horizon nonstandard multiparameter singularly perturbed systems (MSPS) without the nonsingularity assumption that is needed for the existing result are discussed. The new strategies are obtained by solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). Firstly, the asymptotic expansions for the GCMARE are newly established. The main result in this paper is that the proposed algorithm which is based on the Newton's method for solving the GCMARE guarantees the quadratic convergence. In fact, the simulation results show that the proposed algorithm succeed in improving the convergence rate dramatically compared with the previous results. It is also shown that the resulting controller achieves O(∥ μ ∥2n) approximation of the optimal cost. [ABSTRACT FROM AUTHOR]

Accurate phase noise simulation of circuits for radio frequency applications is of great importance during the design and development of wireless communication systems. In this paper, we present an approach based on the Floquet theory for the analysis and numerical computation of phase noise that solves some drawbacks implicitly present in previously proposed algorithms. In particular, we present an approach that computes the perturbation projection vector directly from the Jacobian matrix of the shooting method adopted to compute the steady-state solution. Further, we address some problems that arise when dealing with circuits whose modeling equations do not satisfy the Lipschitz condition at least from the numerical point of view. Frequency-domain aspects of phase noise analysis are also considered and, finally, simulation results for some benchmark circuits are presented. [ABSTRACT FROM AUTHOR]

In this paper, a class of input and output coupled nonlinear systems with multiple equilibria are studied. These kinds of systems can also be viewed as interconnected systems composed of single-input and singlesoutput systems through some linear and nonlinear interconnections. Frequency-domain conditions are established for global convergence and convergence of bounded solutions for such systems. The effects of nonlinear input and output interconnections can be studied through a nonsingular matrix. The design method based on linear matrix inequality for the interconnected matrix is presented. In addition, the relation between input and output coupling here and input transformation in control theory is established. The coupling method is illustrated through a coupled Cbua's circuit. The nonexistence of chaotic attractors or limit cycles in the coupled Chua's circuit can be analyzed by convergence of bounded solutions. [ABSTRACT FROM AUTHOR]

The efforts to find Lyapunov functions for power Systems with losses have been until now in vain. Despite that, engineers have been using approximated energy-like functions to obtain good estimates of the critical clearing lime (CCT) in transient stability analysis of power systems. These approximated energy-like functions are not Lyapunov functions, and are usually obtained by an integration process followed by an approximation of the integration path. Therefore, the good CCT estimates obtained with these functions are not supported by a sound theory. Nevertheless, it is shown in this paper, for a particular approximated energy-like function, a theoretical approach to support these good estimates. The approximated energy-like function studied in this paper is well known in the literature, and was proposed by Athay et al in the COA formulation. It is shown that this approximated energy-like function is neither a Lyapunov function in the usual sense, nor an extended Lyapunov function, when the transfer conductances are taken into account. In spite of that, a function attending the requirements of the extension of the Invariance Principle, that is, an extended Lyapunov function, can be obtained by smooth pertur- bations on that energy-like function. This perturbed function can be used to estimate the attraction area without approximations or conjectures. Indeed, the difference between the proposed extended Lyapunov function and the approximated energy-like function has the order of a smooth perturbation. This fact supports the good CCT estimates that have been obtained using these approximated energy-like functions, and encourages engineers to keep using them for CCT estimates. [ABSTRACT FROM AUTHOR]

The problem of constructing a canonical representation for an arbitrary continuous piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the problem based on a general lattice PWL representation, which can be determined for a given continuous PWL function using existing methods. We first transform the lattice PWL representation into the difference of two convex functions, then propose a constructive procedure to rewrite the latter as a canonical representation that consists of at most η-level nestings of absolute-value functions in n dimensions, hence give a thorough solution to the problem mentioned above. In addition, we point out that there exist notable differences between a lattice representation and the two novel general constructive representations proposed in this paper, and explain that these differences make all the three representations be of their particular interests. [ABSTRACT FROM AUTHOR]

Recently, by replacing the parallel LC “resonator” in Chua's circuit with a lossless transmission line that is terminated by a short circuit, a nonlinear transmission line oscillator is proposed and is named as a “time-delayed Chua's circuit.” In a transmission line oscillator, a linear wave travels along a piece of the transmission line and interacts with terminating electrical components, i.e., a boundary-value problem for a hyperbolic partial differential equation with boundary conditions. Furthermore, a fixed time delay arises due to the propagation time through the transmission line. Delay-induced dynamics are particularly important in technologies where high-speed computers must take into account transmission line effects including propagation delay to prevent undesirable self-oscillations. In this paper, the equation describing Chua's circuit with a lossless transmission line is reduced to a differential-difference equation with one delay (i.e., neutral-type differential equation). By using suitable Lyapunov functionals, we reduce the problem of stability and uniform ultimate boundedness to a scalar ordinary differential inequality. Soon afterwards, we derive conditions for global exponential stability of an equilibrium point. The oscillation of small amplitude in the system are studied by perturbation theory, and a general approach is presented for equations of this type for finding the expansion of the oscillation to any order in terms of the coefficient of the fundamental frequency. The frequency-amplitude relations are derived to second order. Finally, we also give some numerical examples to verify the correctness of our analytic results by computer simulations. [ABSTRACT FROM AUTHOR]

This paper presents an event-driven simulation methodology for injection-locked oscillators. The proposed method adopts a phase-domain macromodel based on a perturbation projection vector (PPV), which expresses the oscillator's phase response using a nonlinear, time-varying differential equation. By expressing the PPV using a piecewise polynomial function, the PPV model can be simulated in an event-driven fashion on a digital logic simulator like SystemVerilog. While this piecewise polynomial approximation introduces a trade-off between the simulation accuracy and speed, our results show that the simulation accuracy quickly reaches its optimal value as the piecewise interval number increases even with first-order polynomials. The experimental results with an LC oscillator, ring oscillator, and burst-mode CDR models operating with both periodic and aperiodic inputs demonstrate that the proposed models achieve speeds up to 2\sim 30\times that of transistor-level Spectre simulations with the same accuracy. [ABSTRACT FROM PUBLISHER]

Several results on instability in nonhomogeneous architectures able to generate Turing patterns are presented. The approach makes use of the continuity theorem regarding the dependence of polynomial roots on coefficients and of the root-locus techniques for small, and large parameter deviations from their homogeneous values, respectively. The results are valid for any linearized nonhomogeneous discrete model capable of generating Turing patterns. [ABSTRACT FROM PUBLISHER]

This paper finds and investigates the application of single-exponential local decay pulse (SELDP) to suppress and induce chaos in a family of nonlinear oscillators subject to weak damping and external periodic excitations. Fourier series of SELDP defined on a period is derived and the approximate series is extended to that defined on the set of whole positive real numbers. To show the feasibility of the obtained results, we first give an effective design scheme of electrical circuit related to SELDP signal and this may be helpful in future implementations. We concentrate on this case in which the unforced system possesses two homoclinic orbits. In order to apply Melnikov's approach to make the underlying parameter conditions for suppressing and inducing chaos more clear, a generic numerical algorithm is proposed to compute complicated Melnikov functions. Two propositions, serving as designing the correct parameters in the SELDP function are also given. From our study, we find that chaos can be induced (suppressed) according to the corresponding Melnikov functions have (do not have) simple zeros. Our work can help to understand the underlying mechanisms of suppressing and inducing chaos. The simulation results show the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a new method to map a state-space continuous-time model into an equivalent discrete state-space model. It is shown that the discrete model can approximate the continuous one to an arbitrary high-order which can be set by the user. In addition, it is demonstrated that the constructed discrete model is guaranteed stable, where it can be run in an A-stable or L-stable mode, depending on the application or user's preference. The proposed mapping method is based on the single-step Obreshkov integration formulas that were proposed to solve ordinary differential equations. Preliminary performance experiments show superior accuracy compared to traditional discretization methods such as the Tustin method. Application of the proposed method to the discretization of analog filters demonstrates a significant accuracy in matching both of the magnitude and phase of the frequency response of the continuous system. [ABSTRACT FROM AUTHOR]

This paper discusses consensus problems for multiagent networks under directed communication graphs. The motions of agents are described by impulsive differential equations, and thus, consensus algorithms can be designed in terms of impulsive systems. Different from the standard consensus algorithms which rely on continuous-time or discrete-time models, the proposed algorithms based on impulsive systems take advantages of instantaneous information. It is shown that the proposed algorithms have a faster convergence speed than the standard consensus algorithms. Moreover, conditions under which all agents reach consensus with the desired performance are presented for the multiagent networks with external disturbances. Simulation results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

A Lyapunov approach is developed in this paper for estimation of the magnitude of self-induced oscillations for systems with piecewise linear elements. The oscillatory trajectories are bounded by invariant level sets of a piecewise quadratic Lyapunov function. An optimization problem with bilinear-matrix-inequality constraints is formulated to minimize the invariant level set and to obtain tight bound for oscillatory trajectories. Several examples demonstrate the effectiveness of the new method on analysis of self-induced oscillations. [ABSTRACT FROM PUBLISHER]

Total ampere-turns of the primary and secondary windings of a transformer are taken as one of variables to analyze the bifurcation behaviors and the border collision phenomenon on voltage-mode-controlled flyback converter. Six operation modes which are separated by the two borderlines of capacitor voltage and the three borderlines of total ampere-turns are obtained. A class of explicit piecewise smooth discrete-time maps with six operation modes is derived to describe the dynamics of the system. The numerical calculations are carried out, the bifurcation diagrams and the maximal Lyapunov exponent spectrums with the control period as a parameter are obtained. Then, the paper particularly analyzes the stability and existence conditions of main periodic orbits. The structure of bifurcation diagrams and the characteristics of operation modes at the border collision points are studied too. Finally, PSIM simulation and experimental results testify the validity of theoretical analysis. [ABSTRACT FROM PUBLISHER]

This paper establishes a discrete-time model and presents an exact method of stability analysis for periodic orbits containing a segment of sliding orbit for switched linear systems. Sliding dynamical equations are obtained by using Utkin's equivalent control method. Sliding mapping and impact mapping are obtained by solving the respective differential equations. A generalized discrete-time mapping for a cycle is derived for three operating scenarios. The coordinates of the periodic orbit points, inflow and outflow sliding regions, and the corresponding Jacobians are obtained. Theoretical analysis and simulation results for a third-order relay-feedback system and a second-order autonomous oscillating circuit are presented to illustrate the proposed model and method. [ABSTRACT FROM PUBLISHER]

Waveform relaxation (WR) is a technique that can be used to solve large systems of ordinary differential equations (ODEs). It is particularly suitable for the parallel solution of ODEs with multiple time scales and has successfully been used for the solution of electronic circuits and for solving partial differential equations. The main issue limiting the utility of WR is the class of problems with strong subsystem-to-subsystem couplings and long analysis time intervals resulting in nonuniform slow convergence. Here, we consider transmission-line (TL) circuits since they represent an important part of a Spice-type circuit solver. For TLs, the coupling between different lines is relatively weak, and thus, partitioning in the transverse direction leads to very fast WR algorithms. However, longitudinal partitioning of TLs is very challenging due to the strong coupling that results. In this paper, we propose an approach with improved convergence properties for strongly coupled longitudinal partitioning of TLs and other similarly strongly coupled circuits. [ABSTRACT FROM AUTHOR]

We construct a coordinate-independent description of oscillator linear response through a decomposition scheme derived independently of any Floquet theoretic results. Trading matrix algebra for a simpler graphical methodology, the text will present the reader with an opportunity to gain an intuitive understanding of the well-known phase noise macromodel. The topics discussed in this paper include the following: orthogonal decompositions, AM-PM conversion, and nonhyperbolic oscillator noise response. [ABSTRACT FROM AUTHOR]

A full wave description of electromagnetic coupling occurring in circuits has to consider time delays. The retarded partial-element equivalent-circuit (rPEEC) method is one of the approaches which allows us to take time delays resulting in a set of neutral functional differential equations into account. Due to the fragility of electromagnetic solvers, the asymptotic stability is a key issue in PEEC modeling. This paper presents an innovative method, based on linear matrix inequalities, to study the input-to-state stability of PEEC models with multiple noncommensurate time delays. Numerical results are given to illustrate the effectiveness oil the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present new results on convergence of a class of nonlinear dynamical systems modeled by the gradients of nonsmooth cost functions. This class of systems arises from neural-network research and can be regarded as a generalization of existing neural-network models. Using the recently developed Lojasiewicz gradient inequality, the convergence analysis of this gradient-like differential inclusion is given. Without assuming the smoothness of the cost function or analyticity of the activation function, we prove the output convergence of the differential system. In addition, for the piecewise analytic activation function with positive first-order derivative, we prove the state convergence. Furthermore, we also discuss the relationship between the convergence rate and the location of terminal limit point. Numerical examples are provided to illustrate the theoretical results and present the goal-seeking capability of the systems. [ABSTRACT FROM AUTHOR]

The dynamics of a zero-average dynamic strategy controlled dc-dc Buck converter, modelled by a set of differential equations with discontinuous right-hand side is studied. Period-doubling and corner-collision bifurcations are found to occur close to each other under small parameter variations. Closer examination of the parameter space leads to the discovery of a novel bifurcation. This type of bifurcation has not been reported so far in the literature and it corresponds to a corner-collision bifurcation of a nonhyperbolic cycle. The bifurcation boundaries are computed analytically in this paper and the system dynamics are unfolded close to the novel bifurcation point. [ABSTRACT FROM AUTHOR]

In this paper, a new design of digital integrator is investigated. First, the trapezoidal integration rule and differential equation are applied to derive the transfer function of the digital integrator. The Richardson extrapolation is then used to generate high-accuracy results while using low-order formulas. Next, the conventional Lagrange finite-impulse response fractional delay filter is directly applied to implement the designed integrator. Two implementation structures are studied: direct substitution and polyphase decomposition. Finally, numerical comparisons with conventional digital integrators are made to demonstrate the effectiveness of this new design approach. [ABSTRACT FROM AUTHOR]

In this paper, we study chaos synchronization in complex networks with time-invariant, time-varying and switching configurations based on the matrix measure of complex matrices. To begin with, we propose an analytical condition for chaos synchronization in complex networks with a time-in- variant configuration. Secondly, we obtain some less conservative synchronization conditions for networks with a time-varying configuration. Thirdly, we consider chaos synchronization in networks with time-average and switching configurations. If complex subnetworks satisfy certain conditions, the networks with time-average and switching configurations are M-synchronizable. At last, we analyze the nonsynchronizability of complex networks. Chaos synchronization in complex networks can't be realized if the coupling configuration and the inner-coupling matrix satisfy certain conditions. Theoretical analysis and numerical simulations verify the effectiveness of the proposed synchronization criteria. [ABSTRACT FROM AUTHOR]

This paper studies stability problems of a class of impulsive systems with time delay whose linear parts contain unstable system matrices. By using the method of variation of parameters, Lyapunov functions and inequalities, several stability criteria are established for both linear and nonlinear impulsive systems with time delay. It is shown that the time delay systems can be stabilized by impulses even if the system matrices are unstable. Several numerical examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

A general circuit-based model of LC oscillator phase noise applicable to both white noise and 1 / f noise is presented. Using the Kurokawa theory, differential equations governing the relationship between amplitude and phase noise at the tank are derived and solved. Closed form equations are obtained for the IEEE oscillator phase noise for both white and 1 / f noise. These solutions introduce new parameters which take into account the correlation between the amplitude noise and phase noise and link them to the oscillator circuit operating point. These relations are then used to obtain the final expression for Voltage noise power density across the output oscillator terminals assuming the noise can be modeled by stationary Gaussian processes. For white noise, general conditions under which the phase noise relaxes to closed-form Lorentzian spectra are derived for two practical limiting cases. Further, the buffer noise in oscillators is examined. The forward contribution of the buffer to the white noise floor for large offset frequency is expressed in terms of the buffer noise parameters. The backward contribution of the buffer to the 1 / Δf² oscillator noise is also quantified. To model flicker noise, the Kurokawa theory is extended by modeling each 1 / f noise perturbation in the oscillator as a small-signal dc perturbation of the oscillator operating point. A trap-level model of flicker noise is used for the analysis. Conditions under which the resulting flicker noise relaxes to an 1 / Δf³ phase noise distribution are derived. The proposed model is then applied to a practical differential oscillator. A novel method of analysis, splitting the noise contribution of the various transistors into modes is introduced to calculate the Kurokawa noise parameters. The modes that contribute the most to white noise and flicker noise are identified. Further, the tail noise contribution is analyzed and shown to be mostly up-converted noise. The combined white and flicker noise model exhibits the presence of a number of corner frequencies whose values depend upon the relative strengths of the various noise components. The proposed model is compared with a popular harmonic balance simulator and a reasonable agreement is obtained in the respective range of validity of the simulator and theory. The analytical theory presented which relies on measurable circuit parameters provides valuable insight for oscillator performance optimization as is discussed in the paper. [ABSTRACT FROM AUTHOR]

The computational complexity of an adaptive filtering algorithm increases with increasing the filter tap length and therefore, the use of such a filter can become prohibitive for certain applications, especially for real-time implementation. In this paper, we develop low-complexity adaptive filtering algorithms by incorporating the concept of partial updating of the filter coefficients into the technique of finding the gradient vector in the hyperplane based on the L∞-norm criterion. Two specific partial update algorithms based on the sequential and M-Max coefficient updating are proposed. The statistical analyses of the two algorithms are carried out, and evolution equations for the mean and mean-square of the filter coefficient misalignment as well as the stability bounds on the step size are obtained. It is shown that the proposed partial update algorithm employing the M-Max coefficient updating can achieve a convergence rate that is closest to that of the full update algorithm. Finally, simulations are carried out to validate the theoretical results and study the convergence rate of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a digital fractional-order differentiator (FOD) is designed by using fractional sample delay. To improve the design accuracy of conventional fractional differencing and Tustin design methods at high frequency regions, the integer delay is replaced by fractional sample delay. By using the well-documented finite-impulse-response Lagrange, infinite impulse response allpass, and Farrow fractional delay filters, the proposed FOD can be implemented easily even though the fractional sample delay is introduced. Several design examples are illustrated to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]