In this paper, time optimal control problems of a class of integrator switched systems with polyhedral state constraint subsets are studied. We first develop a directed graph representation of the system discrete structure. Based on the graph representation, we generate candidate solution paths and propose an algorithm for seeking the optimal solution. A linear programming method for finding the optimal timing information for each path is then proposed. Finally, we report preliminary results on some sufficient conditions and techniques which help reduce the number of candidate paths.
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