Search

Known solvability results for nonlinear index-1 differential-algebraic equations (DAEs) are in general local and rely on the Implicit Function Theorem. In this paper, we derive a global result which guarantees unique solvability on a given time interval for a certain class of index-1 DAEs with certain monotonicity conditions. Based on this result, we show that memristive circuit DAEs arising from the modified nodal analysis are uniquely solvable if they fulfill certain passivity and network topological conditions. Furthermore we present an error estimation for the solution with respect to perturbations on the right-hand side and in the initial value. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The hyperbolicity problem in circuit theory concerns the existence of purely imaginary eigenvalues in the linearization of the time-domain description of the circuit dynamics. In this paper, we characterize the circuit configurations that, in a strictly passive setting, yield purely imaginary eigenvalues for all values of the capacitances and inductances. Our framework is based on branch-oriented, semistate (differential-algebraic) circuit models that capture explicitly the circuit topology, and use several notions and results from digraph theory. So-called P-structures arising in the analysis turn out to be the key element supporting our results. The analysis is shown to hold not only for classical (RLC) circuits but also for nonlinear circuits including memristors and other mem-devices. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]