This article presents a new set representation named the hybrid zonotope. The hybrid zonotope is shown to be equivalent to $2^N$ constrained zonotopes through the addition of $N$ binary zonotope factors and is well-suited for the analysis of hybrid systems with both continuous and discrete states and inputs. The major contribution of this manuscript is a closed-form solution for exact forward reachable sets of linear mixed logical dynamical systems. This is given by a simple identity and does not require solving any optimization programs or taking set approximations. The proposed approach captures the worst-case exponential growth in the number of convex sets required to represent the nonconvex reachable set of a hybrid system while exhibiting only linear growth in the complexity of the hybrid zonotope set representation. To reduce both set representation complexity and the computational burden of reachability analysis, a binary tree is used to store only the combinations of binary factors of the hybrid zonotope that map to nonempty convex sets. The proposed approach is applied to an established benchmark example where the exact reachable set of a discrete-time hybrid system with six continuous and two discrete states is given by a single hybrid zonotope equivalent to the union of 657 constrained zonotopes, and is represented using only 283 continuous factors, 29 binary factors, and 177 linear equality constraints. Furthermore, the hybrid zonotope is closed under linear mappings, Minkowski sums, generalized intersections, and halfspace intersections.
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