## A new LMI condition for robust stability of discrete-time uncertain systems.(English)Zbl 1129.93482

Summary: A new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to show that an interesting result appeared recently is a special case of the proposed condition. Numerical examples also demonstrate the merit of the present condition in the aspect of conservativeness over other results in the literature.

### MSC:

 93D09 Robust stability 93C55 Discrete-time control/observation systems
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### References:

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