Robust performance of a class of control systems

Long Wang

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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...

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Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed...