Robust H∞ control of uncertain systems with two additive time-varying delays

doi:10.1088/1674-1056/24/9/090202

中国物理B ›› 2015, Vol. 24 ›› Issue (9): 90202-090202.doi: 10.1088/1674-1056/24/9/090202

Robust H_∞ control of uncertain systems with two additive time-varying delays

M. Syed Ali, R. Saravanakumar

Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India

收稿日期:2015-03-23 修回日期:2015-04-17 出版日期:2015-09-05 发布日期:2015-09-05
基金资助:
Project supported by the Fund from the Department of Science and Technology of India (Grant No. SR/FTP/MS-039/2011).

Robust H_∞ control of uncertain systems with two additive time-varying delays

M. Syed Ali, R. Saravanakumar

Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India

Received:2015-03-23 Revised:2015-04-17 Online:2015-09-05 Published:2015-09-05
Contact: M. Syed Ali E-mail:syedgru@gmail.com
Supported by:
Project supported by the Fund from the Department of Science and Technology of India (Grant No. SR/FTP/MS-039/2011).

摘要/Abstract

摘要： This paper is concerned with the problem of delay-dependent robust H_∞ control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H_∞ stability criteria are derived in terms of linear matrix inequalities (LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.

关键词: additive time-varying delays, Lyapunov method, H_∞ control, linear matrix inequality

Abstract: This paper is concerned with the problem of delay-dependent robust H_∞ control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H_∞ stability criteria are derived in terms of linear matrix inequalities (LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.

Key words: additive time-varying delays, Lyapunov method, H_∞ control, linear matrix inequality

中图分类号: (Ordinary differential equations)

02.30.Hq

02.30.Ks (Delay and functional equations) 02.30.Yy (Control theory) 05.45.-a (Nonlinear dynamics and chaos)

M. Syed Ali, R. Saravanakumar. Robust H_∞ control of uncertain systems with two additive time-varying delays[J]. 中国物理B, 2015, 24(9): 90202-090202.

M. Syed Ali, R. Saravanakumar. Robust H_∞ control of uncertain systems with two additive time-varying delays[J]. Chin. Phys. B, 2015, 24(9): 90202-090202.

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Robust H_∞ control of uncertain systems with two additive time-varying delays

Robust H_∞ control of uncertain systems with two additive time-varying delays

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