A theorem on the Lyapunov matrix equation
F. T. MAN · IEEE Transactions on Automatic Control · 1969
Given the Lyapunov matrix equationA'P + PA + 2\sigmaQ = 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.