非线性状态空间模型遗忘性研究

动态系统的遗忘性是描述系统行为主要取决于其近期输入的概念，与系统的稳定性、鲁棒性等密切相关。对于非线性状态空间模型，遗忘性在很弱的条件下与整体一致非常吸引等价。系统在凸集或不变区集上的遗忘性可由一类特殊Ｌｙａｐｕｎｏｖ函数的存在性保证。遗忘区域的大小可利用矩阵不等式来估计。

Fading Memory for Nonlinear State Space Models

The property of fading memory(FM) is a concept to characterize the phenomenon of dynamic control systems that the influence of the input long time before the given moment gradually fades out. It is closely related to some essential properties of a control system such as stability and robustness. For the state space models of nonlinear systems, FM is under some mild assumption equivalent to the integral uniform attraction property. A system is of FM on a convex or invariant set if a special Lyapunov function can be constructed. The area of FM can be estimated using the theory of matrix inequality.