Robust Minimum Gain Lemma

The computation of the minimum sensitivity of uncertain Linear Time Invariant (LTI) systems is presented in the paper. The system interconnection is given by a generic Linear Fractional Transformation (LFT) of a nominal model and an uncertain block, where the input-output behavior of the latter is described by Integral Quadratic Constraints (IQC). The extension of the Minimum Gain Lemma is presented for such interconnections, resulting in a convex optimization problem subject to Linear Matrix Inequality (LMI) constraints. With the aim of the Generalized-KYP (GKYP) lemma the minimum gain/sensitivity is computed over a certain finite frequency range. Connection with the already existing literature is highlighted, providing an insight on the obtained results. A numerical example is given to illustrate and validate the proposed methodology.