中立型不确定时滞系统的鲁棒稳定性

Robust stability for uncertain neutral systems with mixed delays

研究中立型不确定时滞系统的鲁棒稳定性问题.系统的不确定性分为非线性不确定性和范数有界不确定性两种情况,构造一个新的Lyapunov-Krasovskii泛函并利用积分不等式对其正定性进行了证明,从而放松了对某些泛函参数的约束;利用Lyapunov方法,基于线性矩阵不等式的形式,分别得到在两种不确定性情况下系统的鲁棒稳定性判据,所得的判据与中立型时滞及离散时滞均相关,从而克服了中立型时滞无关所导致的结论的保守性.通过数值算例表明,所得到的稳定性判据在保守性上优于现存的一些方法.

The robust stability for neutral systems with mixed delays and uncertainties was investigated.The uncertainties under consideration were nonlinear perturbations and norm-bounded uncertainties,respectively.A novel Lyapunov-Krasovskii functional was constructed and its positive definiteness was proved by using integral inequality,which relaxed the constraint on some functional parameters.The neutral-delay-dependent and discrete-delay-dependent stability criteria for two different forms of uncertainty were derived by using Lyapunov method in terms of linear matrix inequalities.Then the conservatism caused by neutral-delay-independence was relaxed.The numerical examples were given to illustrate the effectiveness of the method and the improvement over some existing methods.