Abstract
It is shown that, by the possible use of circuit equivalences, circuits satisfying rather light assumptions possess the semistate description <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{\cal Q} \dot{x} + \cal B(x, t)= \cal D u</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y ={\cal F} x</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u =</tex> input, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y =</tex> output, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x =</tex> semistate, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{\cal Q}, {\cal D} ,{\cal F}</tex> are constant operators. The semistate can be chosen as tree branch voltages and link branch currents; a determination of consistent initial semistates is given which stems from a forward stepping solution equation. An appropriate reduction with attendant signal-flow graph for design is obtained in the linear time-invariant case.
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