Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

• Published in: Mathematical problems in engineering Vol. 2014; no. 2014; pp. 1 - 8
• Main Authors: Ding, Yuanchun, Weng, Falu, Ge, Ji, Liang, Qi, Zhi, Xueyi
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Puplishing Corporation 01.01.2014; Hindawi Publishing Corporation; Hindawi Limited
• Subjects: Closed loop systems; Closed loops; Colleges & universities; Delay; Feedback control; Law; Mathematical models; Regularity; Robust stabilization; Science; Stability; Stabilization; State feedback; Time dependence; Time varying control; Transforms
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2014/796596

The problem of delay-dependent robust stabilization for continuously singular time-varying delay systems with norm-bounded uncertainties is investigated in this paper. First, based on some mathematical transform, the uncertain singular system is described in a form which involves the time-delay integral items. Then, in terms of the delay-range-dependent Lyapunov functional and the LMI technique, the improved delay-dependent LMIs-based conditions are established for the uncertain singular systems with time-varying delay to be regular, causal, and stable. Furthermore, by solving these LMIs, an explicit expression for the desired state feedback control law can be obtained; thus, the regularity, causality, and stability of the closed-loop system are guaranteed. In the end, numerical examples are given to illustrate the effectiveness of the proposed methods.