Adaptive Robust $H_{\infty}$ Control of Time Delay Systems with Unknown Uncertainty Bounds

• Published in: International journal of control, automation, and systems Vol. 10; no. 1; pp. 158 - 165
• Main Authors: Toodeshki, Mojtaba Hosseini, Askari, Javad, Hosseinnia, Saeed
• Format: Journal Article
• Language: Korean
• Published: 2012
• Subjects: time delay systems; uncertain systems; LMI; Adaptive robust $H_{\infty}
• ISSN: 1598-6446; 2005-4092

The problem of adaptive robust $H_{\infty}$ control for uncertain systems with multiple delays is considered in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds are not necessarily known. The objective is to design adaptive robust $H_{\infty}$ state-feedback controller such that the resulting closed-loop system is asymptotically stable and a prescribed $H_{\infty}$ performance level of the closed loop system for disturbance attenuation is guaranteed. To solve this problem, a new sufficient condition is presented in terms of a linear matrix inequality (LMI). The effectiveness of proposed method is verified by its application to an unstable system.