Numerical solution of the discrete-time, convergent, non-negative definite Lyapunov equation

Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation

is called the continuous-time Lyapunov equation and is of interest in a number of areas of control theory such as optimal control and stability (Barnett, 1975; Barnett & Storey, 1968). The equation has a unique Hermitian solution, X, if and only if Xt + X~j ^ 0 for all i and j (Barnett, 1975). In particular if every Xt has a negative real part, so that A is stable, and if C is non-negative defi...

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...

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.

Discrete-time control design with positive semi-definite Lyapunov functions

A useful stability analysis technique from continuous-time nonlinear systems [2] is extended to the discrete-time domain. The result is illustrated on a practical example.