On Multi-Dissipative Perturbations in Linear Systems. Sufficient Conditions for Robust Stability and Performance

Uffe Høgsbro Thygesen and Niels Kjølstad Poulsen

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We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both frequency weighted small gain and passive, and including this in the robustness analysis results in conditions that are less conservative than for instance the small gain criterion. We reduce several robustness analysis questions to Linear Matrix Inequalities: Robust stability, robust stability in presence of parameter uncertainty, robust H-2 performance, and finally robust performance in presence of disturbances with finite signal-to-noise ratio in the sense of Skelton. The corresponding problem of static state feedback controller design reduces to non-convex matrix inequalities, which only in special cases can be transformed to convex ones. We suggest heuristic coordinate descent type algorithms to solve these problems.

IMM Technical Report 1/97

Last modified April 8, 1997

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