State feedback control of piecewise-affine systems with norm bounded noise

Being able to design controllers that are robust to noisy measurements is of fundamental importance in practical applications. With this objective in mind, the original contribution of this paper is to propose a design technique for state feedback control of piecewise-affine systems that is robust to bounded noise in the measurements. More specifically, the paper gives conditions under which a piecewise-affine state feedback controller designed to stabilize a noise-free piecewise-affine system to a target point still stabilizes the system when the state is subject to norm bounded noisy measurements. It will be shown that controllers designed using a globally quadratic Lyapunov function are robust to noisy state measurements and that the state trajectories of the closed-loop system will still converge to a region around the equilibrium point in the presence of noise. The size of this region will be related to the norm bound on the noise.