On the stabilization of linear discrete-time systems

AbstractA 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