The semistate description of nonlinear time-variable circuits

It is shown that, by the possible use of circuit equivalences, circuits satisfying rather light assumptions possess the semistate description {\cal Q} \dot{x} + \cal B(x, t)= \cal D u y ={\cal F} x where u = input, y = output, x = semistate, and {\cal Q}, {\cal D} ,{\cal F} 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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