混合变时延中立型控制系统的鲁棒稳定性新准则

Novel criterion on robust stability for neutral control systems with mixed time-varying delays

研究了具有混合区间变时延和分式不确定性的中立型控制系统的鲁棒稳定性.首先,在系统参数不确定性不存在时,通过构造改进型的Lyapunov-Krasovskii泛函,利用Jesnen积分不等式并引入少量自由权矩阵,综合矩阵凸组合与交互式凸组合等方法,有效估计了Lyapunov-Krasovskii泛函导函数上界,并基于线性矩阵不等式建立了时延相关的渐近稳定性判据.考虑系统参数具有不确定性时,通过引入改进的有界实引理,给出了系统的鲁棒稳定性准则,且易于借助Matlab工具箱中的LMI进行验证.数值算例和比较结果说明该准则的保守性较弱.

The robust stability of neutral control systems with mixed interval time-varying delays and fractional uncertainties is investigated. First, for the system without uncertainties, an improved Lya- punov-Krasovskii functional is constructed. By using the Jesen integration inequality and introducingsome free-weighting matrices, the upper bound of the derivative of the Lyapunov-Krasovskii func- tional is efficiently estimated by combining the matrix convex technique and the reciprocal convex technique and a delay-dependent asymptotical stability criterion is derived based on linear matrix ine-qualities. When the uncertainties are existent, the sufficient condition on robust stability is estab- lished by utilizing the improved bounded real lemma. The conclusion can be checked by the LMI in Matlab toolbox. Finally, the numerical examples and the comparison results show that the conclusionis less conservative than some existent ones.