Abstract: The robust delay-dependent stabilization problem for uncertain singular systems is considered.Delay-dependent stability and stabilization criterions are formulated in terms of Linear Matrix Inequalities（LMIs） by Lyapunov method.A new method that introduces the new free-weighting matrices is proposed to estimate the upper bound of the derivative of the Lyapunov function by considering the additional useful terms which are ignored in previous methods.An algorithm involving convex optimization is proposed to design a fuzzy controller guaranteeing a suboptimal maximal delay such that the system can be stabilized.Two numerical examples are given to demonstrate the effectiveness of the proposed method.

摘要： 研究不确定广义系统的时滞依赖鲁棒镇定问题。利用Lyapunov泛函方法，得到一个线性矩阵不等式（LMIs）形式的时滞依赖稳定与镇定判据。新方法考虑一些以前方法中通常忽略的有用的项，引入一些自由权重矩阵，估计Lyapunov泛函导数的上界；再用凸优化算法，进一步给出状态反馈控制器的设计方法。最后通过两个仿真示例表明了新方法的有效性。