Eigenvalue bounds in the Lyapunov and Riccati matrix equations
David Nicholson · IEEE Transactions on Automatic Control · 1981
Two related theorems of Strang [1] are extended to provide upper and lower bounds on the eigenvalues of the Lyapunov and Riccati matrices, given byQ=AB^{H}+BAandR=AB^{H}+BA+2AHA, whereAandHare Hermitian, positive definite, complex matrices. We discuss inversion to obtain eigenvalue bounds on the matrixAfor the usual case in whichQ , R, andHare known.