Piecewise-linear robust control of systems with input constraints

Robust stabilization of an uncertain system subject to input constraints is addressed without making open-loop stability assumptions. A local approach is taken to find a robust control law and a set of initial conditions that can be stabilized. A piecewise-linear control law generated by a parametrized algebraic Riccati equation of the H_∞ control theory is described. Once system trajectories are sufficiently close to the origin, a certain performance level is ensured through a guaranteed cost control. A simple and tractable design algorithm is proposed and illustrated by a numerical example