The spectrum and eigenspace structure of linear uncertain systems

The authors present a Lyapunov exponents approach to output feedback stabilization of linear systems with time-varying uncertainties. This allows the analysis of precise stability and stabilization radii. These Lyapunov exponents are actually eigenvalues of a certain family of matrices and the corresponding eigenspaces determine the controllability structure. The Lyapunov exponents are numerically computable using optimal control methods. Several results on perturbations of linear differential equations are given. These results are applied to the output feedback stabilization of linear, uncertain systems. Several examples are included