关于非线性大系统的局部状态反馈和稳定区域估计

本文研究了非线性定常大系统利用局部状态反馈的控制以及稳定区域估计问题。文中给出的方法可用来处理较为广泛的系统,特别适合于“最小强相联系统”或具有类似性质的系统。对大型望远镜,应用此方法得到了相当好的结果。

ON LOCAL STATE FEEDBACK AND STABILITY DOMAIN ESTIMATION OF NONLINEAR LARGE SCALE SYSTEMS

It has been a very attractive problem to stabilize large scale system by local state feedback since 1970's. However, this problem has not been solved completely even for linear time-invariant large scale systems, For nonlinear time-invariant large scale systems, most of the researches deal with systems which interconnection gi（x）, i =1, 2, ..., N, among subsystems can be factorized as gi（x）=BiFi（x）, i = 1, 2, ..., N, are the input matrices of the subsystems. Besides, the problem of stability domain estimation was also considered. In this paper, in order to stabilize nonlinear time-invariant large scale systems by local state feedback and to determine its stability domain, linear quadratic design and a technique to define a quadratic Lyapunov function from the positive solution of N decoupled Riccati algebraic equations were employed. The presented method can be used to deal with a wider class of systems without demanding gi（x）=BiFi（x ）. As a result, procedure gives larger stability domain. So, it is possible to achieve a certain stability domain by local state feedback with small gain. For "minimal strongly connected systems" and other systems with similar property, the method is quite effective and the pro-ceduce is simple. As an application to the decentralized stabilization of a large scale telescope, the method here gives better results in comparison with others available in the literatures,