Stabilization on periodic impulse control systems

TL;DR

This paper investigates stabilization methods for linear impulse control systems with periodic impulses, providing characterizations, feedback design strategies, and impulse timing criteria to ensure system stability.

Contribution

It introduces new stabilization characterizations, feedback law design procedures, and impulse timing strategies specifically for periodically impulsed linear systems.

Findings

Characterizations of stabilization conditions

Design methods for feedback laws

Impulse location criteria for stabilization

Abstract

This paper studies the stabilization for a kind of linear and impulse control systems in finite-dimensional spaces, where impulse instants appear periodically. We present several characterizations on the stabilization; show how to design feedback laws; and provide locations for impulse instants to ensure the stabilization. In the proofs of these results, we set up a discrete LQ problem; derived a discrete dynamic programming principle, built up a variant of Riccati's equation; applied repeatedly the Kalman controllability decomposition; and used a controllability result built up in [17].