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The general Liapounov theorem for some degenerate differential systems
International Journal of Statistics and Applied Mathematics · 2017 · Vol. 2(5) · pp. 41–45
Abstract
The aim of this article is to generalize the famous Liapounov Equation: VT + T*V = -2S related to the stationary system : x'(t) = Tx(t), to the general equation A*WB + B*WA = -2S, where S, V, W and are uniformly positive operators, using the spectral theory of the pencil of operators A-B corresponding to the degenerate differential system : Ax'(t) = Bx(t), t>0,where A and B are bounded operators in a Hilbert space.
Differential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsSpectral Theory in Mathematical PhysicsBounded functionMathematicsHilbert spaceDegenerate energy levelsPure mathematicsSpectral theoryDifferential equationMathematical analysisDiscrete mathematicsPhysics
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