On a Solution of the Discrete Time Lyapunov Matrix Equation

Estimates from the discrete-time Lyapunov equation

Bounds for the solution of the discrete algebraic Lyapunov equation

New bounds for solutions of the discrete algebraic Lyapunov equation P = APA T + Q are derived. The new bounds are compared to existing ones and found to be of particular interest when A is non-normal.

Bounds on the trace of a solution to the Lyapunov equation with a general stable matrix

Some new estimates for the eigenvalue decay rate of the Lyapunov equation AX + XA = B with a low rank right-hand side B are derived. The new bounds show that the right-hand side B can greatly influence the eigenvalue decay rate of the solution. This suggests a new choice of the ADI-parameters for the iterative solution. The advantage of these new parameters is illustrated on second order damped...

A new Approximation to the solution of the linear matrix equation AXB = C

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....

Upper bounds for the solution of the discrete algebraic Lyapunov equation

New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P = APAT + Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are computable when the large dimension of A...