Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional
Zhen Cai*,**, and Guozhen Hu**
*Wuhan City Polytechnic University
No.127 Nanli Road, Hongshan District, Wuhan 430064, China
**Hubei Polytechnic University
No.16 Guilin North Road, Xialu District, Huangshi 435003, China
This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.
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