Hard Control Systems Stability Analysis
How is robust stability analyzed for systems with uncertainty?
Answer
Robust stability analysis determines stability despite model uncertainty. Unstructured uncertainty: represented as bounded perturbation, stability checked using Small Gain Theorem (|T|*|Delta| < 1 for stability). Structured uncertainty: use mu (structured singular value) analysis for tight bounds. Parametric uncertainty: Kharitonov's theorem checks interval polynomials, vertex-based analysis for polytopic uncertainty. Robustness margins quantify maximum tolerable uncertainty. Design iteration shapes closed-loop to achieve robust stability and performance despite worst-case uncertainty combinations.
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