On the stabilization of linear discrete-time systems Original Research Article

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 H1 and a matrix H2 such that AH1 + H1A* + BH2* + H2B* > 0; a generalization of the main inertia theorem was also given.