A new discrete-time robust stability condition. (English) Zbl 0948.93058

Summary: A new robust stability condition for uncertain discrete-time systems with convex polytopic uncertainty is given. It enables to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions. It is shown that this new condition provides better results than the classical quadratic stability. Besides the use of a parameter-dependent Lyapunov function, this condition exhibits a kind of decoupling between the Lyapunov and the system matrices which may be explored for control synthesis purposes. A numerical example illustrates the results.


93D30 Lyapunov and storage functions
93D09 Robust stability
93C55 Discrete-time control/observation systems
15A39 Linear inequalities of matrices
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