Stochastic H ₂/H _∞ control for poisson jump-diffusion systems

Abstract

Abstract This paper is concerned with stochastic H ₂/H _∞ control problem for Poisson jump-diffusion systems with (x, u, v)-dependent noise, which are driven by Brownian motion and Poisson random jumps. A stochastic bounded real lemma (SBRL for short) for Poisson jump-diffusion systems is firstly established, which stands out on its own as a very interesting theoretical problem. Further, sufficient and necessary conditions for the existence of a state feedback H ₂/H _∞ control are given based on four coupled matrix Riccati equations. Finally, a discrete approximation algorithm and an example are presented.

Keywords

Poisson jump-diffusion systems / Stochastic H ₂/H _∞ control / Stochastic bounded real lemma / Indefinite stochastic Riccati equation

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