Input-to-state stability

Summary

Input-to-state stability is a stability notion for systems driven by an input, $\dot x = f(x, u)$. It asks that the state decays to a size controlled by the size of the input, whatever the initial state. It merges global asymptotic stability of the unforced system, a strong form of Lyapunov stability, with a bounded-input bounded-state property. It is a basic tool in nonlinear control systems, because it behaves well under cascades and feedback interconnections.