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不确定奇异系统是一类重要的控制系统。为了深入分析一类带非线性扰动的不确定连续时间奇异系统的解的性质及其广义二次稳定性,寻找此类系统广义二次稳定的充分必要条件,首先引入了此类系统广义二次稳定的概念,运用系统状态的坐标变换,利用S-Procedure引理、线性矩阵不等式和Schur补引理,给出了此类系统的解存在且唯一的充分条件,进一步给出了此类系统广义二次稳定的充分必要条件。
Uncertain singular system is an important type of control system. In order to further analyze the properties and the generalized quadratic stability of solutions to a class of singular systems with nonlinear perturbations and to find the necessary and sufficient conditions for the generalized quadratic stability of such systems, The concept of stability, the coordinate transformation of the system state, the existence and unique sufficient conditions for the existence and uniqueness of such systems are given by using the S-Procedure lemma, the linear matrix inequality and the Schur complement. Further more, The necessary and sufficient condition of quadratic stability.