Piecewise-affine state feedback using convex optimization

This paper shows that Lyapunov-based state feedback controller synthesis for piecewise-affine systems can be cast as an optimization problem subject to a set of LMIs analytically parameterized by a vector. Furthermore, it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem without affecting its parameterization structure. Finally, it is shown that piecewise-affine state feedback controller synthesis to maximize the decay rate of a quadratic control Lyapunov function can be cast as a set of quasi-convex optimization problems parameterized by a vector.