H ∞ control for stochastic systems with Poisson jumps

Abstract

This paper discusses the H ∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H ∞ control design is also extended to such systems.