Efficient characterization of contractive coprime factorizations for discrete‐time LPV systems

Abstract This paper provides novel and efficient characterizations for coprime factorizations of discrete‐time polytopic linear parameter‐varying (LPV) systems. The formulation resides in combining poly‐quadratic Lyapunov functions and a variable elimination approach to establish improved synthesis conditions in terms of linear matrix inequalities (LMIs). Unlike the previously existing conditions, the proposed LMI‐based conditions do not rely on methods such as change of variables and slack variables. By doing so, the proposed necessary and sufficient conditions can be achieved such that both contractive right and left coprime factors for LPV systems can be obtained via more computationally efficient and less complex solutions. The effectiveness of the novel synthesis conditions is carried out through a numerical example.