A Lyapunov approach to analysis of discrete singular systems

In this paper, a new type of generalized Lyapunov equation for discrete singular systems is proposed. Then it is applied to studying problems such as pole clustering, controllability and observability for discrete singular systems. First, some necessary and sufficient conditions for pole clustering are derived via the solution of this new type of Lyapunov equation. Further, the relationship between the solution of the Lyapunov equation and structural properties of discrete singular systems is investigated based on these results. Finally, a type of generalized Riccati equation is proposed and its solution is used to design a state feedback law for discrete singular systems such that all the finite poles of the closed-loop systems are clustered into a specified disk.