A modified sensitivity measure for linear digital systems

In this paper a new sensitivity measure for state space systems is proposed. This new measure is a modified form of Tavsanoglu and Thiele's measure but has three advantages: (1) it is more precise than Tavsanoglu and Thiele's measure when the parameters of the state space realizations contain 0 and ±1; (2) it can be used to explain why the sparse Schur and Hessenberg realizations can give better actual sensitivity performance than the corresponding fully parametrized optimal realizations; (3) it is identical with the global round-off noise gain G = tr(QW) + y obtained by Hwang under a dynamic constraint.