  This paper presents methods for using zonotopes and constrained zonotopes to
improve the practicality of a wide variety of set-based operations commonly
used in control theory. The proposed methods extend the use of constrained
zonotopes to represent sets resulting from operations including halfspace
intersections, convex hulls, robust positively invariant sets, and Pontryagin
differences. Order reduction techniques are also presented that provide
lower-complexity inner-approximations of zonotopes and constrained zonotopes.
Numerical examples are used to demonstrate the efficacy and computational
advantages of using zonotope-based set representations for dynamic system
analysis and control.
