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Robust Stability of D-symmetrizable Hyperbolic Systems

100%

Ziółko M. , Białas S.

2001

tom vol. 49, nr 1

167-176

The systems 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 the 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 the conditions type system is a stability of wave propagation. The stability of the 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 hull of stable and D-symmetrizable matrices.

The method of quasilinearization for system of hyperbolic functional differential equations

100%

Karpowicz A.

2008

tom Vol. 48, [Z] 2

155-168

We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations. [zob. pełny tekst: http://www.staff.amu.edu.pl/~commath/papers/482/4825.pdf]