奇异摄动系统的二次稳定性和二次可镇定性

讨论了连续奇异摄动系统的二次稳定性，利用线性矩阵不等式方法，推导了奇异摄动系统二次稳定性的充分条件，并给出了二次可镇定并可解的充分条件和二次可镇定的状态反馈控制器的一种迭代求法．利用MATLAB工具箱仿真验证了结果的正确性．并且和同阶次的正常系统算法进行了有效的比较，论证了奇异摄动方法解决stiff问题的有效性．

Quadratic Stability and Quadratic Stabilizability for Singularly Perturbed System

Quadratic stability is proposed for singularly pe rt urbed continuous systems. Using the linear matrix inequality, a sufficient condi tion is derived for quadratic stability and another sufficient condition is give n for quadratic stabilizability and solvability of singularly perturbed systems. A feedback controller for quadratic stabilization is designed with an iterative algorithm. An example is worked out to illustrate the effectiveness of the meth od and the simulation results are given by the MATLAB tool box. The method is ef fective for stiff questions by comparing with that of regular systems.