Abstract:
The control design techniques for linear or hybrid systems under constraints lead often
to off-line state-space partitions with non-overlapping convex polyhedral regions.
This corresponds to a piecewise affine (PWA) state feedback control laws associated
to polyhedral partition of the state-space.
The aim of this paper is to consider perturbation in the representation of the vertices of such polyhedral regions. Another idea behind this study is to perform a quantization operation on the representation of the state-space regions and the associated
PWA control laws in order to reduce the hardware requirements in terms of processor speed and memory unit. The quantized state-space partitions lose some of the important properties of the explicit controllers: "non-overlapping", "convexity"
and "invariant characterization". The major contribution of this work is to analyze to what extend the non-overlapping
and the invariance characteristics of the PWA controller can be preserved when perturbation takes place on the vertex representation.
Key Words: piecewise affine control, explicit predictive control, robustness.
2010 Mathematics Subject Classification: Primary 52B12; Secondary 52B05, 52B55, 52B70.
