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On quadratic stability of systems with structured uncertainty

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2 Author(s)
Yan, W.-Y. ; Sch. of Electr. & Comput. Eng., Curtin Univ. of Technol., Perth, WA, Australia ; Lam, J.

This paper considers the problem of stability robustness with respect to a class of nonlinear time-varying perturbations which are bounded in a component-wise rather than aggregated manner. A family of robustness bounds is parameterized in terms of a non-singular symmetric matrix. It is shown that the problem of computing the largest robustness bound over the set of non-singular symmetric matrices can be approximated by a smooth minimization problem over a compact set. A convergent algorithm for computing an optimal robustness bound is proposed in the form of a gradient flow

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Automatic Control, IEEE Transactions on  (Volume:46 ,  Issue: 11 )