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Circuits and Systems, IEEE Transactions on

Issue 12 • Date December 1976

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Displaying Results 1 - 21 of 21
  • Editorial

    Publication Year: 1976 , Page(s): 693
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    Freely Available from IEEE
  • Input-output stability theory of interconnected systems using decomposition techniques

    Publication Year: 1976 , Page(s): 714 - 729
    Cited by:  Papers (20)
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    We study the input-output stability of arbitrary interconnections of nonlinear, time-varying, multivariable subsystems which may be either continuous-time or discrete-time. All subsystems are specified by their input-output description. We use an algorithmic decomposition of the overall system into a hierarchy of strongly connected subsystems (SCS) interacting through inter-connection subsystems (IS). Theorem I establishes that the overall system is stable once the SCS's and the IS's are stable. Theorem II shows that, under very reasonable assumptions, these sufficient conditions are actually necessary. Using the concept of minimum essential set, we partition each SCS into two parts: one part corresponds to the "forward subsystem" whose only feedbacks are self-loops; the other part corresponds to the vertices of the minimum essential set; together they form the overall feedback system. Simplified stability conditions for the SCS are obtained by exploiting this structural decomposition. Theorem III gives sufficient condition for stability of nonlinear time-varying SCS's. The other three theorems consider linear time-invariant continuous-time, lumped as well as distributed SCS's. We provide translation rules for reformulating these three theorems for the discrete-time case. We also show how to reduce the amount of calculation involved in finding the SCS characteristic polynomial. View full abstract»

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  • Some new results on decomposition and pivoting of large sparse systems of linear equations

    Publication Year: 1976 , Page(s): 729 - 738
    Cited by:  Papers (2)
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    Some new results are presented concerning the decomposition and pivoting of large sparse systems of linear equations. The paper uses graph theoretical reasoning. Starting point are some results of Rose on triangulated graphs, separation sets, and optimal ordering of sparse matrices. In the paper it is proven that a graph (and thus at the same time the matrix it represents) can be "split" ("torn") by certain vertex sets (unknowns) such that the overall number of "fill-ins" may still be optimum, although ordering is done in all components (submatrices) separately and almost independently. The results may have some significance for very large systems where they may assist in cutting down on set up time. Also some impact on the study of the possible benefits of using more than one floating point processor in parallel may be expected. View full abstract»

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  • Sparse matrix techniques for the shortest path problem

    Publication Year: 1976 , Page(s): 752 - 758
    Cited by:  Papers (1)
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    Two methods of implementing computer programs for solving the shortest path problem are presented. By symbolic processing, a computer program generates another program or an address table which represents an optimal shortest path algorithm, in the sense that only nontrivial operations required for a given particular network structure are executed. The implementation methods presented here are powerful when a network of fixed sparseness structure must be solved repeatedly with different numerical values. View full abstract»

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  • Solution of large-scale networks by tearing

    Publication Year: 1976 , Page(s): 706 - 713
    Cited by:  Papers (41)  |  Patents (3)
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    A generalized method of tearing, or diakoptics, for solving large-scale networks is derived. The idea of diakoptics is viewed as simply the partition of branches and the Kirchhoff laws. A solution algorithm based on LU decomposition is presented. If the network may be "torn apart," then the computations at the subnetwork level can be carried out independently. We present an example which is a family of networks with a parameter p and show that diakoptics, compared to the conventional network analysis, sometimes saves computations and sometimes requires more computations. View full abstract»

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  • Dynamic allocation of hierarchical information paths for the organization of interconnected systems

    Publication Year: 1976 , Page(s): 814 - 817
    Cited by:  Papers (1)
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    A technique is presented for dynamically selecting the "best" path for disseminating information throughout a network on the basis of assigning ranks to the nodes and demerits to the links. One possible application of this technique is in the selection of paths for disseminating precise time information throughout a network from the best nodal clock to nodes whose clocks have less precision. The method uniquely defines and iteratively selects the path of least demerit from each node to the highest ranking node regardless of the initial conditions or perturbations to the network structure. View full abstract»

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  • Mathematical models for the circuit layout problem

    Publication Year: 1976 , Page(s): 759 - 767
    Cited by:  Papers (6)
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    In this paper mathematical models for use in a topological approach to solving the circuit layout problem are outlined. After a brief survey of some existing models, an improved model is suggested. This model is based on the concept of partially oriented graph and contains more topological information than earlier models. This reduces the need for special constraints on the graph embedding algorithm. The models also allow pin and gate assignment in function of the layout under certain conditions. View full abstract»

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  • A note on bipartite graphs and pivot selection in sparse matrices

    Publication Year: 1976 , Page(s): 817 - 821
    Cited by:  Papers (2)
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    In this note a bipartite graph representation is proposed for the study of pivot strategies on sparse matrices. Using this representation, an algorithm which fullfills the Brayton's condition for Gaussian elimination optimality has been devised. View full abstract»

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  • A latent macromodular approach to large-scale sparse networks

    Publication Year: 1976 , Page(s): 745 - 752
    Cited by:  Papers (20)  |  Patents (4)
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    Two major topics are discussed: macromodularity and latency. The macromodular approach uses the tearing procedure, modified nodal analysis, symbolic LU factorization techniques, and separate updating and convergence tests, to take full advantage of large sparse networks with highly repetitive subnetworks. An efficient algorithm requiring only the updating of a small portion of the Jacobian matrix when individual solution vectors do not converge is presented, and the storage requirements and computation efforts to obtain a complete solution are estimated. The latent approach takes advantage of the temporary cessation of network activity between stimulation and response through knowledge of actual stimulation and the history of the internal node voltages. This approach is fully utilized by defining latent directed paths. A "latent graph" theory is proposed, and some results are presented. View full abstract»

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  • Optimal-aim control strategies applied to large-scale nonlinear regulation and tracking systems

    Publication Year: 1976 , Page(s): 800 - 806
    Cited by:  Papers (9)
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    Several optimal-aim control strategies for large-scale nonlinear regulation and tracking systems are discussed. A theorem concerning explicit optimal-aim control laws with adaptive-feedback implementations, an example of its application to a transient power-system model, and a qualitative comparison of the optimal-aim strategy and a classical optimalcontrol strategy for a linear harmonic-oscillator model are given. View full abstract»

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  • Stability of flows of a dynamic flow network

    Publication Year: 1976 , Page(s): 826 - 829
    Cited by:  Papers (1)
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    The need for a network model for the purpose of study of stability of flows is first discussed. A dynamic flow-network model is then presented. It has applications to power networks. A two-matrix transformation method is used to find a suitable Liapunov function. Stability conditions are then obtained when some constraints are imposed on the dynamic components and on the connectivity of the network. The conditions are like a circle criterion, which are on the bounds of the conductances, the memoryless components of the network. View full abstract»

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  • A floating via router based on a saturated zone strategy

    Publication Year: 1976 , Page(s): 829 - 835
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    This letter describes a new routing algorithm which is oriented towards floating via technology in a two-sided environment. The algorithm builds up "saturated zones" of interconnections and then combines these saturated zones by four tactics which attempt to complete a maximum number of paths selected from a restricted set of path shapes. A router based on this algorithm has been implemented, and has averaged 99.4 percent completion on 24 Illiac IV boards, and attained 100 percent completion on a large printed wiring board. The router averages about one via per wire, uses modest storage, and is generally economical. View full abstract»

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  • Line removal algorithms for graphs and their degree lists

    Publication Year: 1976 , Page(s): 778 - 782
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    An important and basic characterization of a graph is the sequence or list of degrees of that graph. Problems regarding the construction of graphs with specified degrees occur in chemistry and in the design of reliable networks. A list of nonnegative integers is called graphical if there is a graph (called a realization) with the given list as its degree list. The usual algorithms for determining whether a given list is graphical are derived from the effect on a graphical list of the removal of a point from a graph. After reviewing such an algorithm by Havel-Hakimi and its generalization by Wang and Kleitman, we develop a corresponding algorithm based on the removal of a line from a graph. We conclude by reviewing and providing simple proofs of algorithms for a list to be multigraphical due to Hakimi and Butler. The conditions relating a graphical or multigraphical list to the point and line connectivity of their realizations, due to Edmonds, Wang and Kleitman, Boesch and McHugh, and Hakimi, are presented along with new and simple proofs of the multigraph case. View full abstract»

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  • A two levels algorithm for tearing

    Publication Year: 1976 , Page(s): 783 - 791
    Cited by:  Papers (8)
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    This paper deals with tearing methods for the solution of a large scale system of linear algebraic equations. A modification algorithm Is presented and evaluated with respect to other available techniques, namely, Householder's formula and Bennet's algorithm. Then, an optimization problem related to the "best" way of tearing a given matrix A with a certain associated structure is stated and solved by proving it to be equivalent to the determination of a minimum essential set of a suitably defined hypergraph H . A branch-and-bound algorithm for minimum essential set in H , based on a number of local reduction rules is outlined. Finally, the application of the obtained results to the tearing problem is discussed and its complexity compared with LU decomposition method. View full abstract»

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  • Diakoptic and generalized hybrid analysis

    Publication Year: 1976 , Page(s): 694 - 705
    Cited by:  Papers (14)  |  Patents (3)
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    Two elementary approaches are presented for analyzing large-scale linear resistive networks by first tearing them apart, solving the torn subnetworks separately, and then interconnecting the results to obtain the solution of the overall network. The first approach makes use of elementary graph- and circuit-theoretic concepts and leads to a unified formulation which includes all existing versions of diakoptic analysis based on Kron's original ideas as special cases. The second approach consists of an appropriate partitioning of the network elements and a manipulation of the linear algebraic equations into the form of a generalized hybrid analysis involving a matrix having a bordered block-diagonal structure. These two distinct approaches are shown to be equivalent in the sense that the first is a special case of the second. The result is then extended to nonlinear networks, where an efficient computational algorithm is presented which takes full advantage of sparse matrix techniques and is compatible with parallel computations. View full abstract»

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  • Reliability of packet switching broadcast radio networks

    Publication Year: 1976 , Page(s): 806 - 813
    Cited by:  Papers (2)  |  Patents (31)
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    Packet switching broadcast radio networks are receiving considerable attention as a feasible solution for applications involving fast network deployment requirements, inaccessible physical environments, and mobile communication devices. Such networks also offer economic alternatives to traditional multiplexing schemes for local distribution. Routing algorithms which enable point-to-point packet transportation have been developed for broadcast radio networks. It appears that a routing algorithm becomes more efficient when the number of alternate paths are restricted; on the other hand, reliability considerations suggest increasing the number of alternate paths. In this paper, we study and compare the reliability of broadcast radio networks for different routing algorithms. View full abstract»

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  • Linearized Bayesian estimation of network flows

    Publication Year: 1976 , Page(s): 823 - 826
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    Suppose we have an imprecise estimate of arc flows in a given network, either through prior measurements under similar conditions, or through observation of related phenomena; how can we use imprecise measurements of boundary flows into and out of the network to improve our original estimate? This is a problem in Bayesian regression that is difficult to carry out, in general. However, by using a linearized approach due to credibility theory that is similar to results in linear filter theory, one can find interesting and useful estimates using only first and second moments of the prior and observation error distributions. This result has application in road and communication traffic measurement, statistical auditing, and nuclear material accountability problems. View full abstract»

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  • The multilayer routing problem: Algorithms and necessary and sufficient conditions for the single-row, single-layer case

    Publication Year: 1976 , Page(s): 768 - 778
    Cited by:  Papers (37)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1336 KB)  

    The multilayer routing problem is introduced and its relation to the single-row single-layer routing problem is illustrated [1], [2]. An easily implementable sufficient condition on the routability of a net list over a single row of nodes is presented. The solution is given by a constructive forward marching procedure and the result is an improvement over the worst-case prediction of So [1]. The implementation algorithm is programmed on CDC 6400 computer. The nature of the optimum criterion relating to single-row routability is investigated and a necessary and sufficient condition is given to characterize the nature of optimality. Some necessary conditions are also presented which can be used to evaluate the sufficient condition and served as a lower bound for the channel capacity in the routing problem. The more general routing problem is illustrated and possible future research directions are discussed. View full abstract»

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  • On minimum multigraphs with prescribed lower bounds on local line connectivities

    Publication Year: 1976 , Page(s): 821 - 823
    Cited by:  Papers (1)
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    Multiple path requirements for networks with integer line capacities (multigraphs) can be stated in a very general form by a reliabilIty matrix R , where r(i,j) is the specified lower bound on the number of line-disjoint paths between points \upsilon _{i} and \upsilon _{j} in the multigraph. In light of the classical "max-flow, min-cut" theorem, this is equivalent to specifying local line connectivities. This paper presents a new and conceptually simple algorithm for constructing minimum size (total number of lines) multigraphs which satisfy the requirements specified in a reliability matrix. View full abstract»

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  • Sparse Hessenberg reduction and the eigenvalue problem for large sparse matrices

    Publication Year: 1976 , Page(s): 739 - 744
    Cited by:  Papers (1)
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    A four-stage algorithm for the efficient solution of the standard eigenvalue problem for large sparse matrices is presented. The matrix whose eigenvalues are desired is first reduced to a block upper triangular form, if possible, to expose those eigenvalues that are readily identified. The reduced matrix Is then scaled and transformed to a sparse Hessenberg matrix with numerical stability control. Laguerre's iteration is then used to find the remaining eigenvalues. Examples are given. View full abstract»

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  • An efficient algorithm for simulation on transients in large power systems

    Publication Year: 1976 , Page(s): 791 - 799
    Cited by:  Papers (1)
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    The simulation of the transient response of a large interconnected power system involves the solution of a very large system of differential-algebraic equations under a great variety of initial conditions and disturbances. The demands imposed on a digital transient stability program to i) study larger power system interconnections, ii) provide a more detailed representation of the power system components, and iii) permit the simulation of longer time periods, have the effect of increasing the computing time. The importance of, and the need for, efficient computational schemes is apparent. The method presented in this paper makes detailed use of the structural properties of the differential-algebraic system representation. The nonlinear differential-algebraic system is split into a nonstiff part with long time constants coupled to a stiff part with a sparse Jacobian matrix whose longest time constant is shorter than that of the first part. These two parts are linear in their respective states, i.e., the system is semilinear. With the nonstiff part removed, a smaller set of stiff equations with a smaller conditioning number than the original system is obtained. Consequently, longer stepsizes can be used so as to reduce the computation time. The proposed multistep integration schemes exploit the stiffness and semilinearity properties. Numerical results on a small test problem indicate that these schemes operate with good accuracy at stepsizes as large as 100 times those necessary to ensure numerical stability by more conventional schemes. View full abstract»

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