Selection of state variables for locally solvable nonlinear networks

Abstract

AbstractThis paper considers the necessary and sufficient condition for the state variables for locally solvable nonlinear networks to be capacitor currents vector iC and inductor voltages vL, (iCT, vLT), instead of capacitor charges vector q and inductor fluxes vector ψ (qT, ψT). the condition is given by the regularity of matrix K and |ta, vj|→∞ as |e, j|→∞ in the resistance network where all the capacitors and inductors are replaced by voltage sources e and current sources j, respectively. Here, ie and vj are the voltage source current and current source voltage, respectively.As a result, in the networks where (qt, ψt) can be transformed into (iCT, vLT), the network dynamics can be described in the same way as in a linear system and global consideration on networks can be done only by investigating the property of matrix KA. For example, the sufficient condition for the equilibrium point to be globally asymptotic‐stable is given comparatively easily, the consideration on eventual passivity can be done easily, and, in general, there exist various analysis methods such as in the case where (qT, ψT) are used as state variables.