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A result on common quadratic Lyapunov functions
2003
IEEE Transactions on Automatic Control
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In this note, we define strong and weak common quadratic Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the nonexistence of a strong CQLF, for a pair of LTI systems, is characterized by easily verifiable algebraic conditions. These conditions are found to play an important role in proving the existence of strong CQLFs for general LTI systems. Index Terms-Quadratic stability, stability theory, switched linear systems.
doi:10.1109/tac.2002.806661
fatcat:e3bxspdlsjgnbmwjw4z2v6nm44