Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 47, Issue 11, Pages 1926-1930Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2002.804463
Keywords
Lyapunov equation; singular systems
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In this note, we revisit the Lyapunov theory for singular systems. There are basically two well-known generalized Lyapunov equations used to characterize stability for singular systems. We start with the Lyapunov theorem of the work by Lewis. We show that the Lyapunov equation of that theorem can lead to incorrect conclusion about stability. Some cases where that equation can be used are clarified. We also show that an attempt to correct that theorem with a generalized Lyapunov equation similar to the original one leads naturally to the generalized equation of Takaba et al.
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