A generalization of an inequality of Coppel
Gary A. Hewer · Proceedings of the American Mathematical Society · 1974
Upper and lower bounds for the solutions of a linear ordinary differential equation are determined from the solutions of upper and lower matrix comparison equations. The coefficients of the comparison equations are computed with the help of Lozinskiĭ’s logarithmic “norm” \[ l ( A ) = lim h → + 0 [ | I + h A | − 1 ] / h , l(A) = \lim \limits _{h \to + 0} [|I + hA| - 1]/h, \] and the concept of the “matricial norm” as a matrix of scalar norms. Using these estimates some new criteria for the stability of composite systems are obtained.