Upper bounds for the solution of the discrete algebraic Lyapunov equation

New upper bounds for the solution of the discrete algebraic L yapunov equation (DALE) P = APAT + Q are presented. The only restriction on their applicability is thatA be stable; there are no restrictions on the singular values o f A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability ofA. The upper bounds are computable when the large dimension of A make direct solution of the DALE impossible. The new bounds a re shown to reflect the dependence of P onA better than previously known upper bounds.

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