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A Lyapunov approach to analysis of discrete singular systems. (English) Zbl 0987.93036
Summary: A new type of generalized Lyapunov equation for discrete singular systems is proposed. Then it is applied to study 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 to this new type of Lyapunov equation. Further, the relationship between the solution to the Lyapunov equation and the structure properties of discrete singular systems will be 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.

##### MSC:
 93B55 Pole and zero placement problems 93C55 Discrete-time control/observation systems
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##### References:
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