离散广义系统稳定半径的研究

Research on stability radius of generalized discrete time systems

广义矩阵到达不稳定的距离可由系统矩阵束确定.首先定义了离散广义状态系统的稳定半径,并给出了到由正则因果且指数不超过1的矩阵束产生的不稳定距离的计算式,最后将其转化为矩阵的最小奇异值的问题来求解.

The concept of ＂distance to instability＂ of a matrix is generalized to system pencils.In this paper a suitable measure of the stability radius of a generalized discrete state-system is defined,and a computable expression for the distance to instability is derived for regular causal pencils of index less than or equal to one.At last the problem has been solved by converting it into the problem of minimizing the smallest singular value of a certain matrix.