The problem of bounding the states of a linear time varying hybrid system at fixed transition times where the mode sequence is allowed to vary is considered. It is shown via an illustrative example that a simple decomposition algorithm produces weak bounds which get worse as the number of epochs increases. To address this issue, a novel algorithm is proposed, based on solving families of relaxed linear programming problems, which allows the incorporation of additional constraints derived from physical insight. This provides tighter bounds while avoiding explicit enumeration of all possible mode trajectories.
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