带执行器饱和的单输入系统不变椭圆的一种解析描述

给出了一个椭圆为执行器饱和单输入系统的收缩不变集的一个充分必要条件.该条件利用二次不等式的形式给出.该二次不等式的系数由反馈增益矩阵,系统矩阵和椭圆形状所确定.如果该椭圆是不变椭圆,通过解该二次不等式可以得到该椭圆的最大半径.给出的方法直接并且是解析的.在一定的条件下,该二次不等式可以转化成线性矩阵不等式,从而可以用有效的数值方法求解.数值例子验证了方法的有效性.

An analytical characterization of invariant ellipsoid for single input linear systems with input saturation

A new necessary and sufficient condition for an ellipsoid to be an invariant set of a linear system under bounded linear feedback is presented. The condition is given analytically in terms of a quadratic inequality with its coefficient determined by the prescribed state feedback gain and the given ellipsoid. Also, the maximal ellipsoid that is invariant can be calculated analytically by solving the quadratic inequality. This proposed condition is direct and analytical and thus allows us to give some insight into the saturated linear systems. Under a condition, the quadratic inequality condition can also be converted into an LMI condition. A numerical example shows the validity of the proposed method.