A procedure for analyzing a class of nonlinear semistate equations that arise in circuit and control problems

Some circuits not possessing a state-variable represenation may admit semistate equations of the formAx(t)+B(x(t))=f(t)wherex,fare vector functions,Ais a singular constant matrix, andBis a nonlinear vector valued function. Some nonlinear optimal control problems, in which certain combinations of controls are either "cheap" or free, also lead to equations in this form. In this paper we show how In many cases of interest It is possible to solve a singular linear subsystem and use this solution to reduce the problem to a smaller order nonsingular, nonlinear system.