This article describes an algorithm for solving electrical networks which consist of linear and nonlinear resistors and independent sources, and where the characteristics of each of the resistors is described by a function Gk(?),i = Gk(v), where Gk(?) is continuous, monotonically increasing, piecewise linear, and one‐to‐one from (—∞, ∞) onto (—∞, ∞), and where k is an index which spans all the resistors in the network. The solution is found by solving successively equivalent linear networks which represent the nonlinear network locally and which correspond to a “solution curve.” Essential to the efficiency of the computation process is the method of modifying matrices which enables the process to find the inverse of a conductance matrix by modifying another matrix rather than by matrix inversion. The algorithm provides a fast computation method for both of the following two cases: (1.) the network contains both linear and nonlinear resistors and (2.) the sources are functions of time and the solution is required for successive values of time. In the latter case the algorithm computes each solution from the previous one rather solving each case independently.

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This article considers the stability of n-input.-u-output, linear time invariant convolution feedback systems. Stability theorems arc expressed in terms of the Nyquist plots of the eigenvalues of 0(8) where 8 varies along the Nyquist contour in the complex plane and 0(8) is the t.ransfer function of the open loop system which is allowed. to have poles in the right half plane. Our objectives are to state clearly these theorems and to prove them. The paper investigates the geometry of the eigenvalues in the complex plane; in particular, the properties of the eigenvalues on and near the exceptional points, and the graph theoretic properties of the loci of the eigenvalues are studied. The stability theorems are proved using these geometric properties.

This article considers the question of existence and uniqueness of the response of nonlinear time‐varying RLC networks driven by independent voltage and current sources. It is proved that under certain conditions the response exists, is unique, and is defined by a set of ordinary differential equations satisfying some Lipschitz conditions. These conditions are of two types: (1) the network elements must have characteristics which satisfy suitable Lipschitz conditions and (2) the network must satisfy certain topological conditions. It should be noted that elements with nonmonotonic characteristics are allowed and that the element characteristics need to be continuous but not differentiable.

Project Objectives:To develop new computer representations and reasoning mechanisms that ]!4 enable intelligent systems to autonomously design, monitor, and understand > complicated physical systems, through appropriate mixtures of numerical a. and symbolic computing. dWAs part of this research we demonstrated novel computational tools that 0-00 autonomously monitor, understand, and control complex physical systems. -0 _ These tools understand the models, monitor the execution of the simulations, and formulate qualitative explanations of the results. These tools interact I with their human users in symbolic terms, allowing them to specify qualita-I •, tive goals for measurement and intelligent control applications.Work started under this effort is now being continued at MIT, Yale, University of Colorado at Boulder, Perdue, Xerox, and Hewlett Packard. Over the last three years five of our recent graduates have received National Young Investigator awards, largely based on their work on this project. ITIC.ZllUI- 94-29806,(