Discrete‐time state‐feedback control of polytopic LPV systems

Abstract This paper focuses on a new state‐feedback control synthesis for discrete‐time polytopic linear parameter‐varying (LPV) systems. The synthesis conditions have been derived using an approach less conservative than those currently found in the literature, which allows to deal with polytopic LPV systems subject to time‐varying parameters in all matrices of its state‐space representation. Based on parameter‐dependent Lyapunov functions, a set of linear matrix inequalities‐based conditions is provided to obtain a discrete‐time state‐feedback controller. Another significant advantage of the proposed conditions is the ability to include the poly‐quadratic condition as a particular case, presenting a solution to this so far unresolved problem. In addition, using the same concept, an improved condition for quadratic control synthesis is given. Finally, the effectiveness of the proposed state‐feedback control design method is assessed and compared to that of similar approaches by means of numerical examples.