Quadratic Stability and Singular SISO Switching Systems

@article{Shorten2009QuadraticSA,
  title={Quadratic Stability and Singular SISO Switching Systems},
  author={Robert Shorten and Martin J. Corless and Kai Wulff and Steffi Klinge and Richard H. Middleton},
  journal={IEEE Transactions on Automatic Control},
  year={2009},
  volume={54},
  pages={2714-2718}
}
In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A-ghT, and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product A(A-ghT) . The technical note also contains a spectral characterization of strictly… CONTINUE READING

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