Robust control for uncertain linear systems via polyhedral Lyapunov functions

This paper deals with the robust stabilization problem for uncertain linear systems. We use the class of the polyhedral norms, or more generally that of the polyhedral gauge functions, as candidate Lyapunov functions. These functions have the noteworthy property that if the problem of stabilizing a certain system can be solved via Lyapunov functions and a continuous state feedback control, then there exist a polyhedral Lyapunov function and a piecewise-linear control which solve the problem. A synthesis technique to construct the control and the Lyapunov function is proposed