一类中立型时滞系统新的鲁棒稳定性准则

New Robust Stability Criterion for a Class of Neutral Time-delay Systems

本文考虑了一类具有时变时滞和非线性扰动的中立型系统的鲁棒稳定性问题.基于Lyapunov稳定性理论和自由权矩阵方法,得到保证系统鲁棒渐近稳定的新的充分条件.所得结果同时依赖于离散时滞和中立时滞,并用LMIs表示.由于对Lyapunov泛函导数采用了无保守的估计,因此所得结果具有较小的保守性,能够给出时变时滞较大的允许时滞上界.作为一个特例,我们也给出了缺少中立时滞的系统的鲁棒稳定性准则.数值例子表明了所得到结果的有效性.

This paper considers the robust stability problem for a class of neutral systems with time-varying delays and nonlinear perturbations. Based on the Lyapunov stability theory and the free-weighting matrix method, a new sufficient condition is obtained, which can guarantee the robust asymptotic stability of the systems. The derived result depends on both discrete delay and neutral delay, and is expressed by LMIs. Because of using the non-conservative estimation of the derivative of Lyapunov functional, the derived result is less conservative, and can give larger allowable upper bounds of time-varying delays. As a special case, we present the robust stability criterion of the systems in absence of neutral delay. Numerical example shows the effectiveness of obtained results.