Singularity conditions for the non-existence of a common quadratic Lyapunov function for pairs of third order linear time invariant dynamic systems |
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Authors: | Christopher King |
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Institution: | a Department of Mathematics, Northeastern University, Boston, MA 02115, USA b The Hamilton Institute, NUI, Maynooth, Co. Kildare, Ireland |
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Abstract: | The condition that a finite collection of stable matrices {A1, … , AM} has no common quadratic Lyapunov function (CQLF) is formulated as a hierarchy of singularity conditions for block matrices involving a number of unknown parameters. These conditions are applied to the case of two stable 3 × 3 matrices, where they are used to derive necessary and sufficient conditions for the non-existence of a CQLF. |
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Keywords: | Stability theory Convex cones Lyapunov equation |
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