A PROCEDURE FOR ANALYZING A CLASS OF NON-LINEAR SEMISTATE EQUATIONS THAT ARISE IN CIRCUIT AND CONTROL-PROBLEMS

Some circuits not possessing a state-variable representation may admit semistate equations of the form Ax(t) plus B(x(t)) equals f(t) where x, f are vector functions, A is a singular constant matrix, and B is 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. The possibility to solve a singular linear subsystem in many cases of interest is shown. This solution is used to reduce the problem to a smaller order nonsingular, nonlinear system.