Abstract
A pair of matrices ( A, B), where A is p × p and B is p × q, is said to be positive stabilizable if there exists X such that A + BX is positive stable. In a previous paper, it was noticed that Lyapunov’s criterium on matrix stability can be generalized as follows: ( A, B) is positive stabilizable if and only if there exist a positive definite matrix H 1 and a matrix H 2 such that AH 1 + H 1 A * + BH 2 * + H 2 B * > 0; a generalization of the main inertia theorem was also given.
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