LMI conditions for robust stability of 2D linear discrete-time systems.

Hmamed, A.; Alfidi, M.; Benzaouia, A.; Tadeo, F.

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Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties

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In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying...

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Simple conditions for robust stability of positive discrete-time linear systems with delays

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Rank-one LMI approach to robust stability of polynomial matrices

Didier Henrion, Kenji Sugimoto, Michael Šebek (2002)

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Necessary and sufficient conditions are formulated for checking robust stability of an uncertain polynomial matrix. Various stability regions and uncertainty models are handled in a unified way. The conditions, stemming from a general optimization methodology similar to the one used in $μ$ -analysis, are expressed as a rank-one LMI, a non-convex problem frequently arising in robust control. Convex relaxations of the problem yield tractable sufficient LMI conditions for robust stability...