Explicit solution of 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.

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...

Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic ∗

We investigate the solution of the Lyapunov equation with the matrix sign function method. In order to obtain the factorized solution we use a partitioned Newton iteration, where one part of the iteration uses formatted arithmetic for the hierarchical matrix format while the other part converges to an approximate full-rank factor of the solution.

The Descriptor Discrete–time Riccati Equation: Numerical Solution and Applications∗

We investigate the numerical solution of a descriptor type discrete–time Riccati equation and give its main applications in several key problems in robust control formulated under very general hypotheses: rank compression (squaring down) of improper or polynomial systems with L∞–norm preservation, (J, J ′)–spectral and (J, J ′)–lossless factorizations of a completely general discrete–time syste...