带非线性扰动的不确定多时滞系统时滞相关鲁棒稳定性

摘要

利用矩阵不等式技巧,得到了一个新的具非线性时变扰动的不确定多状态时滞系统的鲁棒稳定性判据.系统中的时滞是未知定常的,时变参数的不确定项是范数有界的,而非线性扰动项满足一定的线性约束.基于矩阵不等式技巧和Lyapunov泛函方法,得到了以线性矩阵不等式(LMI)形式给出的时滞相关鲁棒稳定性判据.最后,通过两个示例表明,与文献方法相比,采用文中所提方法可减少结果所存在的保守性,证明了文中方法的有效性.%A new robust stability criterion for uncertain systems with multiple state-delays and nonlinear time-varying perturbations is obtained by the matrix inequality technique. In these systems, the delays are unknown constant, the time-varying parameter uncertainties are norm-bounded and the nonlinear perturbations meet certain linear constraints. Then, on the basis of matrix inequality technique and Lyapunov functional, a delay-dependent robust stability criterion expressed as LMI (Linear Matrix Inequality) is established. It is finally shown by two examples that, compared with the methods presented in the literatures, the method presented in this paper can reduce the conservativeness of the results, which indicates the validity of the proposed method.