李亚普诺夫方程解的奇异值和鲁棒稳定性

SINGULAR VALUES IN THE SOLUTION OF LYAPUNOV EQUATION AND ROBUST STABILITY

本文首先导出了李亚普诺夫方程A^TP+PA=-Q解的奇异值下界。然后,基于这一下界,导出了由状态方程x=Ax+Bu描述的线性定常系统鲁棒渐近稳定的一个充分条件。

This paper considers the lyapunov Equation ATP+PA = - Q where, A∈R'×'is nonsingular, P∈R'×' is symmetric and Q∈Rn×'is symmetric positive definite or positive semidefinite. For this a fundamental inequality which demonstrates lower bounds for the singular values of P, is established. Then, based upon this fundamental inequality, a sufficient condition for robust stability of linear time-invarint systems described dy the state equation X = Ax + Bu is given.