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| Stochastic H2 / H∞ Control for Poisson Jump-Diffusion Systems |
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Citation： |
Meijiao WANG.Stochastic H2 / H∞ Control for Poisson Jump-Diffusion Systems[J].Chinese Annals of Mathematics B,2016,37(5):643~664 |
| Page view： 1380
Net amount： 1253 |
Authors： |
Meijiao WANG; |
Foundation： |
This work was supported by the Special Funds of the
National Natural Science Foundation of China (No.11426154). |
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| Abstract： |
This paper is concerned with stochastic $H_{2}/H_{\infty}$ 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 $H_{2}/H_{\infty}$ 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 $H_{2}/H_{\infty}$
control, Stochastic bounded real lemma, Indefinite stochastic
Riccati equation |
Classification： |
93E20, 60H10, 93B36, 49N10 |
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