  Piecewise affine (PWA) systems are widely applied in many practical cases
such as the control of nonlinear systems and hybrid dynamics. However, most of
the existing PWA control methods have poor scalability with respect to the
number of modes and system dimensions and may not be robust to the disturbances
in performance. In this paper, we present a robust approximate simulation based
control method for PWA systems under bounded external disturbances. First, a
lower-dimensional linear system (abstraction) and an associated interface are
designed to enable the output of the PWA system (concrete system) to track the
output of the abstraction. Then, a Lyapunov-like simulation function is
designed to show the boundedness of the output errors between the two systems.
Furthermore, the results obtained for linear abstraction are extended to the
case that a simpler PWA system is the abstraction. To illustrate the
effectiveness of the proposed approach, simulation results are provided for two
design examples.
