A Kronecker Based Theory for Robust Root Clustering of Linear State Space Models with Real Parameter Uncertainty

In this paper, the problem of matrix root clustering in subregions of complex plane for linear state space models with real parameter uncertainty is considered. An existing theory for nominal matrix root clustering using Kronecker Matrix Algebra is extended to the perturbed matrix case and bounds are derived on the perturbation norms to maintain root clustering inside a given region. The theory allows us to get an explicit relationship between the parameters of the root clusterinlg region and the uncertainty region of the parameter space. The current literature available for robust stability becomes a special case of this unified theory. The proposed analysis is much less conservative compared to the existing methods because it is specifically tailored to real parameter uncertainty.