Matrix Uncertainty Structures for Robust Stabilizability

Consider a linear state equation whose system matrices contain time-varying uncertainties. Furthermore, assume that the values of these parameters are unknown but bounded. The goal is to develop a single linear time-invariant state feedback which stabilizes the system for all admissible uncertainties. In this work, such results are achieved by exploiting the structure of the uncertainty. Structure of the uncertainty is concerned with "where" the uncertainty enters the system matrices and which matrix entries can "tolerate" arbitrarily large perturbations. The main result gives sufficient conditions for stabilizing uncertain multi-input systems. Via these conditions, one can stabilize systems which cannot be handled by existing stabilizability criteria. An example to this effect is given in the sequel. Moreover, the class of systems which satisfy this new criteria captures those systems satisfying the so-called "matching condition."