Topological Conditions For The Unique Solvability Of Linear Time-Invariant And Time-Varying Networks
INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS(1987)
Abstract
The problem of knowing whether the non-unique solvability depends on the particular values of the components or on their topological interconnections is studied for linear networks with arbitrary, time-invariant as well as time-varying n-ports.
Within every network, the topological notions of its sockets and of their independence are introduced. Networks with independent sockets are shown-at least when there are no relations among the non-zero coefficients, nor repetitions of the same coefficient are allowed, i.e. under suitable generality assumptions-to be uniquely solvable. Networks with dependent sockets are shown to be never uniquely solvable.
Polynomially bounded algorithms, requiring only integer arithmetic, to test independence are available. When independence fails, a topological configuration of components which shows fewer topologically independent variables than equations, is proved to exist.
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Key words
linear time invariant
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