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

Robust Approximate Simulation for Hierarchical Control of Piecewise Affine Systems under Bounded Disturbances