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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.
A necessary and sufficient condition is given for a shrinkage invariant set of elliptic actuator saturated single input systems. The condition is given by the form of quadratic inequality whose coefficients are given by the feedback gain matrix, the system matrix and the elliptical shape . If the ellipse is an invariant ellipse, the maximum radius of the ellipse can be obtained by solving the quadratic inequality. The given method is directly and analytically. Under certain conditions, the quadratic inequality can be transformed into a linear matrix Inequality, which can be solved by numerical method. Numerical examples show the effectiveness of the method.