Necessary Conditions for Feedback Passivation of Nonaffine-in-Control Systems

It is well understood that an open-loop Lyapunov stable nonaffine-in-control nonlinear system can be asymptotically stabilized through feedback. But stabilizing an open-loop unstable nonaffine system remains an open research question. This paper derives the necessary conditions required to render a general open-loop unstable nonlinear system passive through static feedback. It is shown that this is possible only if the system under consideration has relative degree one and is weakly minimum phase through an appropriate output definition. Unlike feedback passivation for affine-incontrol nonlinear systems this result is not sufficient. The developments and the essential ideas of the paper are verified for a continuously stirred tank reactor.