Stabilization of uncertain systems with norm bounded uncertainty using control Lyapunov functions

A robust stabilization problem in a state-space setting is treated. It is assumed that the states are available for feedback. Using a fixed-Lyapunov-function approach (quadratic stability) it is shown that an open-loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear time-invariant state-feedback controller. As a consequence, it is shown that the existence of a quadratically stabilizing nonlinear time-varying dynamic state-feedback controller implies the existence of a quadratically stabilizing memoryless linear time-invariant state-feedback compensator