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. The pathwise state-feedback impulsive mechanism is shown universal in that any asymptotically stabilizable system admits such impulsive control law making the system stable. To improve the system performance, we establish some conditions the optimal impulse instants should satisfy using variational method, and design gradient-based algorithms to search for optimal impulse instants. A schematic algorithm is further designed to compute a series of parameters and construct a new and better impulsive control law. Finally, a numerical example shows the efficiency of the proposed approach.