LMI relaxations for non-quadratic discrete stabilization via Pólya Theorem

In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of Polya´s Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.