Estimates from the discrete-time Lyapunov 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 for solutions of the discrete algebraic Lyapunov equation

A family of sharp, arbitrarily tight, upper and lower matrix bounds for solutions of the discrete algebraic Lyapunov are presented. The lower bounds are tighter than previously known ones. Unlike the majority of previously known upper bounds, those derived here have no restrictions on their applicability. Upper and lower bounds for individual eigenvalues and for the trace of the solution are fo...

Positive 2D Discrete-Time Linear Lyapunov Systems

Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

A NEW LYAPUNOV EQUATION FOR DISCRETE - TIME DESCRIPTOR SYSTEMS ' Jog 0

For discrete-time descriptor syslems, various generalized Lyapunov equations were studied in the literature. Howevn these well known generalized Lyapunov equations can be used only under some restrictive assumptions on the plant (as system regularity, or positiveness of a Q matrix, for example). To overcome these limitations, we propose in this paper a new generalized Lyapunov equation for disc...