A new Lyapunov equation for discrete-time descriptor systems

For discrete-time descriptor systems, various generalized Lyapunov equations were studied in the literature. However, 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 discrete-time descriptor systems.