A theorem on the Lyapunov matrix equation |
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| Authors: | Man F. |
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| Affiliation: | University of Toronto, Toronto, Canada; |
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| Abstract: | Given the Lyapunov matrix equationA'P + PA + 2sigmaQ = 0where σ is some positive scalar, a necessary and sufficient condition for the real parts of the eigenvalues ofAto be less than -σ is thatP - Qis negative definite. The condition provides an upper bound to the solution of the Lyapunov matrix equation and is useful in the design of minimum-time or minimum-cost linear control systems. |
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