Universal controllers for robust control problems (Q1377568)

The concept of a robust control Lyapunov function is defined for a class of uncertain single-input nonlinear systems. It is shown that if there exists a \(C^2\) robust control Lyapunov function, then a globally asymptotically stabilizing state-feedback control law can be constructed. A formula for this control law in terms of the nominal system data, the control Lyapunov function and the uncertainty bounds is given. The controller is continuously differentiable outside the origin \(0\), and under the extra assumption that the robust control Lyapunov function has the so-called ``small control property'', continuity at \(0\) is guaranteed.