I want to pinpoint the times where an output waveform of an electronic circuit has a specific value. This is a root-finding problem but to my knowledge root finders don't guarantee to find all roots at once. (Actually I only need the root that occurs first.)
The state variable equations of the circuit (A, B, C and D matrices) and waveform expressions based on the exponential matrix are available and therefore it's natural to use a Newton-Raphson based method. However, it would be possible to generate the companion matrix and polynomial transfer functions, and maybe that is a better (faster) approach (when it guarantees finding the earliest root).
My problem is not being sure of how the roots and zeros of a transfer function and/or the eigenvalues of a (companion) matrix relate to the zero-crossings of a non-steadystate time-domain waveform. Does the fact that a transfer function assumes the zero-state solution is absent invalidate the companion matrix approach?
