Controlled Invariance for Nonlinear Systems

Necessary and sufficient conditions are derived for "(A, B)-invariance," called here controlled invariance, for nonlinear systems x˙ = f(x, u). The obtained results generalize and elucidate already known results about systems x˙ = A(x)-Σmi=1 uiBi(x). A new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given.