Extremum principles for the analysis of nonlinear network systems

In this article, based on the idea of two interconnected semi-flows in network systems for the transfer of matter or energy, new principles of extremum are proven for the main problem of network analysis. On this basis, the Wood-Charles method of non-Newtonian linearization of the network analysis problem has been refined and generalized. The method differs from existing ones in that it is effective when starting from any point. The presented theorems and method are applicable to nonlinear network systems with lumped parameters, and, in particular, to gas, heat, oil and water supply networks.