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Circuits and Systems, IEEE Transactions on

Issue 11 • Date November 1980

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Displaying Results 1 - 14 of 14
  • Editorial

    Publication Year: 1980 , Page(s): 981 - 982
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  • On the stability and well-posedness of interconnected nonlinear dynamical systems

    Publication Year: 1980 , Page(s): 1097 - 1101
    Cited by:  Papers (7)
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  • Constructive stability and asymptotic stability of dynamical systems

    Publication Year: 1980 , Page(s): 1121 - 1130
    Cited by:  Papers (76)
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    In an earlier paper, the authors presented an algorithm for constructing a Liapunov function for a dynamical system. In this paper, we present theorems which allow the algorithm to be used In proving the asymptotic stability of dynamical systems, both difference and differential equations. The notion of an asymptotically stable set of matrices is introduced, and is shown to be a sufficient condition for the algorithm's termination in a finite number of steps. The instability stopping criterion is strengthened and the efficiency of the algorithm is improved in a number of ways. We investigate the tightness of our method by applying it to two-dimensional systems for which necessary and sufficient conditions for stability are known. View full abstract»

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  • Dynamic nonlinear networks: State-of-the-art

    Publication Year: 1980 , Page(s): 1059 - 1087
    Cited by:  Papers (51)
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    This paper surveys the state-of-the-art of the qualitative aspects of nonlinear RLC networks. The class of networks being surveyed may contain multi-terminal and multi-port RESISTORS, INDUCTORS, AND CAPACITORS, as well as dc and time-dependent voltage and current sources. The concepts of impasse points and local solvability are introduced and shown to be of fundamental importance in modeling a physical network. Simple criteria are given which guarantee the existence of a global state equation. General theorems are presented for identifying or testing whether a dynamic nonlinear network possesses one or more of the following basic qualitative properties: 1. No finite-forward-escape-time solutions. 2. Local asymptotic stability of equilibrium points and observability of operating points. 3. Eventual uniform-boundedness of solutions. 4. Complete stability and global asymptotic stability. 5. Existence of a dc or periodic steady-state solution. 6. Unique steady-state response and spectrum conservation. The hypotheses of most of these theorems are couched in graph- and circuit-theoretic terms so they can be easily checked, often by inspection. Special efforts are made to state the concepts and results in a form that can be easily understood and used by the nonspecialist. Moreover, each concept and property is profusely illustrated with carefully conceived examples, and intuitive explanations so as to make this paper both motivating and somewhat self-contained. Extensive references are provided to facilitate researchers interested in conducting future research on the many unsolved problems in dynamic nonlinear networks. View full abstract»

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  • On the response of nonlinear multivariable interconnected feedback systems to periodic input signals

    Publication Year: 1980 , Page(s): 1088 - 1097
    Cited by:  Papers (5)  |  Patents (1)
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    In this paper, we study the response of a large class of nonlinear multivariable feedback systems to periodic input signal. Specifically, we study the existence, uniqueness, boundedness, and periodicity of a large class of feedback systems which may be modeled by means of a class of Volterra integral equations (including delay systems). We also study the distortion effects in such systems due to nonlinearities. In our approach, we address those multivariable systems which may be viewed as interconnected systems. Our results are phrased in terms of the qualitative properties of (hopefully simpler) subsystems and in terms of the properties of the system interconnecting structure, and they make use of easily interpreted graphical frequency-domain techniques. The method of proof of the main results uses a novel technique of combining boundedness results and an invariance principle for integral equations. View full abstract»

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  • Hierarchical stability and alert state steering control of interconnected power systems

    Publication Year: 1980 , Page(s): 1102 - 1112
    Cited by:  Papers (21)
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    A state-space model of an interconnected power system having both generator and load nodes is proposed. The resulting system of equations is interpreted as the degenerate limit of a singularly perturbed system. The model is used to derive a condition for the (local) asymptotic stability of an equilibrium. This condition decomposes in an intuitive way for subsystems interconnected via a backbone network. The model is used to formulate the problem of steering the power system from a postdisturbance alert state to a secure state, and a solution to the steering problem is also proposed. View full abstract»

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  • On the topology of FET circuits and the uniqueness of their dc operating points

    Publication Year: 1980 , Page(s): 1045 - 1051
    Cited by:  Papers (8)
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    We show here how to prove several results which make it possible to deduce whether or not many common FET circuits can possess more than one, or only one, dc operating point, as a consequence of their topological structure alone. These results extend to FET circuits some similar results which have recently been proved for circuits containing bipolar transistors. View full abstract»

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  • A nonlinear state decomposition

    Publication Year: 1980 , Page(s): 1113 - 1121
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    An axiomatic state model for nonlinear operators on a Hilbert resolution space is constructed. We use it to show that the structure (transition operators and isomorphism theorems) of nonlinear operators has much in common with that of linear operators. In addition to the structure, the principle of optimality is shown to carry over. View full abstract»

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  • Nonlinear networks and Onsager-Casimir reversibility

    Publication Year: 1980 , Page(s): 1051 - 1058
    Cited by:  Papers (12)
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    Time-invariant networks composed of transformers, linear resistors, and nonlinear reactive elements are studied, and it is shown that the usual noise model for the resistors implies that in an inductorless network, the capacitor charges have, as random processes, a microscopic reversibility property, and more generally, the capacitor charges and inductor fluxes have a generalized reversibility property, provided that the capacitor or inductor characteristics have odd symmetry. View full abstract»

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  • Chaotic motion in nonlinear feedback systems

    Publication Year: 1980 , Page(s): 990 - 997
    Cited by:  Papers (31)
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    New criteria are found which imply the existence of chaos in R^n . These differ significantly from criteria previously reported in the mathematics literature, and in fact our methods apply to a class of systems which do not satisfy the hypotheses of the usual theorems on chaos in R^n . The results are stated in such a way as to preserve the flavor of many well-known frequency-domain stability techniques. The results provide easily verifiable criteria for the existence of chaos in systems which are of dimension greater than one. View full abstract»

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  • A best approximation framework and implementation for simulation of large-scale nonlinear systems

    Publication Year: 1980 , Page(s): 1005 - 1014
    Cited by:  Papers (42)
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    A conceptual and mathematical framework is presented for optimally approximating a large-scale continuous-time-parameter nonlinear dynamical system S_C by a continuous-time-parameter model \hat{S}_C as well as a discrete-time-parameter model \hat{S}_D , which can be readily simulated respectively on an analog and on a digital computer. A reproducing kernel Hilbert space approach in appropriate weighted Fock spaces is used in the problem formulation and solution. Assuming that the input-output map of the system S_C can be represented by a Volterra functional series V_t , belonging to a Fock space F_{\underline {\rho}}(E) , the input-output maps for the simulators \hat{S}_C and \hat{S}_D are obtained as "best approximations" in F_{\underline {\rho}}(E) for the entire (untruncated) series V_t . Each of these models has the following features: (a) It is adaptive because it is based on a set of test input-output pairs which can be incorporated in the system by on-line multiplexing, (b) it is optimal in the sense of being a projection in a Hilbert space of nonlinear operators, (c) it is easily implementable by means of a set of interconnected linear dynamical systems and zero-memory nonlinear functions of single variables, and (d) unlike polynomic (truncated Volterra series) approximations, it constitutes a global approximation and thus is valid under both small- and large-signal operating conditions. View full abstract»

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  • Global inverse function theorems

    Publication Year: 1980 , Page(s): 998 - 1004
    Cited by:  Papers (5)
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    It is often of interest to determine whether it is possible to invert a given mapping f of one subset of R^n into another. This paper reports on a collection of pertinent results and related material. We first prove a theorem which is used in latter sections of the paper. It provides several characterizations of a homeomorphism between open subsets of R^n . Corresponding results are then proved for C^k -diffeomorphisms Another theorem, one of our main results, shows that a C^k map f between two spaces of a certain general type is a C^k -diffeomorphism if and only if a certain steepest descent process can always be carried out, and for each y converges globally to a unique solution x of f(x)=y . A final section is concerned with specific results for mappings that take one open rectangular region in R^n into another. These results are of direct interest, for example, in the area of economics, where they provide definitive invertibility conditions for a large class of price-demand relations. View full abstract»

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  • Dynamics of the Van der Pol equation

    Publication Year: 1980 , Page(s): 983 - 989
    Cited by:  Papers (12)
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    This paper is a review of approaches to understanding "chaotic" dynamics in the forced Van der Pol equation. In addition, it discusses the phenomena of entrainment and phase locking from the point of view of dynamical systems theory. There are two principal regions of the parameter space where chaotic motion has been analyzed. The first occurs in a nearly linear system near resonance. Here one uses the method of averaging to initially reduce the problem to a two-dimensional one. This two-dimensional problem is analyzed by using bifurcation theory and topological methods. The appearance of homoclinic orbits in the averaged equations signals the presence of more complicated dynamics for the original problem. The second region of parameter space one examines is the one in which the Van der Pol equation describes a relaxation oscillation. In this situation one can approximate the dynamics by the iteration of a noninvertible one-dimensional mapping. This process is described together with the use of symbolic dynamics in parametrizing the resulting limit sets. View full abstract»

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  • Device modeling via nonlinear circuit elements

    Publication Year: 1980 , Page(s): 1014 - 1044
    Cited by:  Papers (72)
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    Two basic approaches to device modeling are presented. The physical approach consists of 4 basic steps: 1) device physics analysis and partitioning, 2) physical equation formulation, 3) equation simplification and solution, and 4) nonlinear network synthesis. The black-box approach consists also of 4 basic steps: 1) experimental observations, 2) mathematical modeling, 3) model validation, and 4) nonlinear network synthesis. Each approach is ilustrated with 2 examples: Gunn Diode and SCR for the physical approach and Hysteretic Inductor and Memristive Device for the black-box approach. While the techniques for carrying out the first 3 steps in each approach presently involve more art than science, a unified theory for carrying out the last step (nonlinear network synthesis) is beginning to emerge. In particular, the universe of all lumped nonlinear circuit elements can now be classified into algebraic and dynamic elements via a completely logical axiomatic approach. Contrary to what is the case in linear circuit theory, it is shown that an infinite variety of basic algebraic and dynamic elements will be needed in the eventual formulation of a unified theory on device modeling. Consequently, these elements are given a complete and in-depth treatment in this paper. This material can also be regarded as a self-contained survey of the state-of-the-art on nonlinear network synthesis. View full abstract»

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