Abstract
This paper studies the stabilization for a kind of linear and impulse control system in finite-dimensional space 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, derive a discrete dynamic programming principle, build up a variant of Riccati's equation, apply repeatedly the Kalman controllability decomposition, and use a controllability result built up in [S. Qin and G. Wang, J. Differential Equations, 263 (2017), pp. 6456--6493].
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