Abstract
AbstractThe critical direction theory for analysing the robust stability of uncertain feedback systems is generalized to include the case of non‐convex critical value sets, hence making the approach applicable for a much larger class of relevant systems. A redefinition of the critical perturbation radius is introduced, leading to the formulation of a Nyquist robust stability measure that preserves all the properties of the previous theory. The generalized theory is applied to the case of rational systems with an affine uncertainty structure where the uncertain parameters belong to a real rectangular polytope. Necessary and sufficient conditions for robust stability are developed in terms of the feasibility of a tractable linear‐equality problem subject to a set of linear inequalities, leading ultimately to a computable Nyquist robust stability margin. A systematic and numerically tractable algorithm is proposed for computing the critical perturbation radius needed for the calculation of the stability margin, and the approach is illustrated via examples. Copyright © 2001 John Wiley & Sons, Ltd.
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