Robust Stability of D-symmetrizable Hyperbolic Systems

摘要

The syntems under consideration are governed by a set of first-order linear partial differential hyperbolic equations together with boundary conditions.The Lyapunov method is used to verify the stability of the initial-boundary value problem.Necessary and sufficient conditions for stability are obtained under the assumption that the matrix coefficients in the differential equations and in teh boundary conditions are D-symmetrizable.The considered systems have an interesting property: Hurwitz type stability and Schur type stability occur in one system simultaneously.The stability of teh continuous type system is a stability of wave propagation.The stability of teh discrete type system is a stability of the boundary feedback and the boundary reflections.Necessary and sufficient conditions for the robust stability of an initial-boundary value problem are obtained for the case where the matrix coefficients belong to a convex hul of stable and D-symmetrizable matrices.