Abstract
This work focuses on the absolute stability problem of Lurie control system with interval time-varying delay and sector-bounded nonlinearity. Firstly, we present a refined Wirtinger's integral inequality and establish an improved Wirtinger-type double integral inequality. Secondly, a modified augmented Lyapunov-Krasovskii functional (LKF) is constructed to analyze the stability of Lurie system, where the information on the lower and upper bounds of the delay and the delay itself are fully exploited. Based on the proposed integral inequalities and some bounding techniques, the upper bound of the derivative of the LKF can be estimated more tightly. Accordingly, the proposed absolute stability criteria, formulated in terms of linear matrix inequalities, are less conservative than those in previous literature. Finally, numerical examples demonstrate the effectiveness and advantage of the proposed method.
| Original language | English |
|---|---|
| Pages (from-to) | 2422-2437 |
| Number of pages | 16 |
| Journal | International Journal of Robust and Nonlinear Control |
| Volume | 29 |
| Issue number | 8 |
| Early online date | 12 Mar 2019 |
| DOIs | |
| Publication status | Published - 25 May 2019 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019 John Wiley & Sons, Ltd.
Funding
This work was supported in part by the National Natural Science Foundation of China under Grants 61773081, 61860206008, and 61833013 and in part by the Technology Transformation Program of Chongqing Higher Education University under Grant KJZH17102, the Science and Technology Plan of Beijing Municipal Education Commission under Grant KM201910017002, and the NSFC under Grant 11771024.
Keywords
- absolute stability
- linear matrix inequalities (LMIs)
- Lurie systems
- time delay