Some applications of the differential inequalities technique, in the analysis of nonlinear circuits

Applications of the differential inequalities technique for estimation (bounding) of solutions of nonlinear circuits and systems are considered. A theorem that gives results for a general class of nonlinear circuits (both autonomous and nonautonomous) for which the linear and nonlinear parts can be distinguished is given. For the class of systems whose state matrices satisfy the quasi-monotonicity condition and for which the nonlinearities intervene only in diagonal elements, it is always possible to give bounds in terms of solutions of linear upper and lower systems. The more general case when the above-mentioned assumptions are not satisfied is also discussed, and some examples of applications are included