Stability and induced ℓ2-gain of MIMO input-output LPV systems

This paper considers the problem of assessing the stability and the induced ℓ₂-gain of a class of Linear Parameter-Varying (LPV) systems in input-output form with affine parameter dependence. Based on a polynomial method developed recently, where the a priori choice of a central polynomial plays a critical role, sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed which reduce conservatism in comparison with an existing approach. Based on Linear Matrix Inequalities (LMIs), the problem is solved where the choice of the central polynomial is optimized. To show the usefulness of the proposed approach, a comparison with the existing technique is given.