Stabilization of Uncertain Linear Systems

Feedback stabilization of linear, uncertain systems is usually analyzed using quadratic Lyapunov functions that are common to all values in the uncertainty set. In this paper we use the alternative classical concept of Laypunov exponents to characterize the precise (exponential) stability regions for systems with contrained linear output feedback. In particular, we exploit the continuity of the maximal Lyapunov exponent depending on the size of the uncertainty and on the bounds of the feedback gain matrix, to obtain results on the exponential stabilizability radius r(u) as a function of the linear, time invariant feedback u. Several examples show, among other facts, that quadratic Lyapunov functions lead in general to conservative criteria, when compared to the precise exponential stabilizability region.