Stabilization and optimization of linear systems via pathwise state-feedback impulsive control

In this work, we address the stabilization and optimization issues for a class of linear systems in terms of pathwise state-feedback impulsive control. We show that the pathwise state-feedback impulsive mechanism is universal in that any asymptotically stabilizable system admits such an impulsive control law. Furthermore, to improve the system performance, we solve a min-max problem of optimizing the impulsive paths via proper algorithm design. A numerical example illustrates the efficiency of our proposed method.