Conditions for the 2-D characteristic polynomial of a matrix to be very strict Hurwitz

Conditions for the bivariate characteristic polynomial of a matrix to be very strict Hurwitz are presented. These conditions are based on the necessary and sufficient conditions for the existence of positive definite solutions to the 2-D continuous Lyapunov equation. It is shown that such an existence is only sufficient but not necessary for the characteristic polynomial to be very strict Hurwitz. Further, the testing of zeros at infinite distant points requires the use of a class of very strict positive real functions.<
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