Abstract
In this paper, we further develop the generalized Lyapunov equations for discrete-time descriptor systems given by Bender. We associate a stable discrete-time descriptor system with a Lyapunov equation which has unique solution. Furthermore, under the assumptions of reachability and observability, the solutions are guaranteed to be positive definite. All results are valid for causal and noncausal descriptor systems. This provides a unification of Lyapunov equations and theories established for both normal and descriptor systems. Based on the developed Lyapunov equation, a Riccati equation is also obtained for solving the state-feedback stabilization problem.
Published Version
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