Quadratic Stabilization and Control of Piecewise-Linear Systems

A. Hassibi and S. Boyd

Proceedings of American Control Conference, 6:3659-3664, June 1998.

We consider analysis and controller synthesis of piecewise-linear systems. The method is based on constructing quadratic and piecewise-quadratic Lyapunov functions that prove stability and performance for the system. It is shown that proving stability and performance, or designing (state-feedback) controllers, can be cast as convex optimization problems involving linear matrix inequalities that can be solved very efficiently. A couple of examples are included to demonstrate applications of the methods described.