# Composite Robust $$H_\infty$$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer

## Abstract

In this paper, the robust stochastic stabilization and robust H1 control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, in control input channel, a composite control scheme is proposed by integrating the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation and disturbance rejection performance can be achieved. A numerical example is provided to show the potential of the proposed techniques.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1489249

- Report Number(s):
- PNNL-SA-125771

Journal ID: ISSN 0018-9286

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Transactions on Automatic Control

- Additional Journal Information:
- Journal Volume: 63; Journal Issue: 12; Journal ID: ISSN 0018-9286

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- H-infinite index, Stochastic control, observers

### Citation Formats

```
Liu, Yunlong, Wang, Hong, and Guo, Lei.
```*Composite Robust $H_\infty$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer*. United States: N. p., 2018.
Web. doi:10.1109/TAC.2018.2819683.

```
Liu, Yunlong, Wang, Hong, & Guo, Lei.
```*Composite Robust $H_\infty$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer*. United States. doi:10.1109/TAC.2018.2819683.

```
Liu, Yunlong, Wang, Hong, and Guo, Lei. Mon .
"Composite Robust $H_\infty$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer". United States. doi:10.1109/TAC.2018.2819683.
```

```
@article{osti_1489249,
```

title = {Composite Robust $H_\infty$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer},

author = {Liu, Yunlong and Wang, Hong and Guo, Lei},

abstractNote = {In this paper, the robust stochastic stabilization and robust H1 control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, in control input channel, a composite control scheme is proposed by integrating the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation and disturbance rejection performance can be achieved. A numerical example is provided to show the potential of the proposed techniques.},

doi = {10.1109/TAC.2018.2819683},

journal = {IEEE Transactions on Automatic Control},

issn = {0018-9286},

number = 12,

volume = 63,

place = {United States},

year = {2018},

month = {1}

}