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Hybrid controllers for tracking of impulsive reference state trajectories: a hybrid exosystem approach

We study the problem of designing controllers to track state trajectories for plants with jumps in the state that are given by constrained differential equations capturing the continuous dynamics and constrained difference equations (or inclusions) capturing the discrete dynamics. The reference trajectories consist of signals having intervals of flow and instantaneous jumps, and are generated via a known hybrid exosystem. The class of controllers considered are hybrid and are designed to guarantee that the jump times of the plant coincide with those of the given reference trajectories. By recasting the tracking problem as the stabilization of a set and using asymptotic stability tools for time invariant hybrid systems, we derive sufficient conditions for the closed-loop system that guarantee tracking of reference trajectories.