Simultaneous eigenvalue lower bounds for the Riccati matrix equation

The author derives n simultaneous lower bounds on the sums of the eigenvalues of the solution of the algebraic Riccati equation and of the Lyapunov matrix equation. These bounds extend the single inequalities shown in the literature for the trace and for the maximum eigenvalue. Two inequality versions are derived and evaluated for application purposes, and a comparison to relevant bounds in the literature is given.<
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