On discrete‐time LPV control using delayed Lyapunov functions

Abstract

Abstract This paper presents new stabilization conditions for discrete‐time linear parameter‐varying systems in the form of linear matrix inequalities. The use of Lyapunov functions with dependence on delayed scheduling parameters is introduced. In addition, a lifted condition based on a Lyapunov function with dependence on delayed scheduling parameters, constructed in terms of an augmented state vector that takes into account a generic number of higher‐order shifted states, is presented. Numerical examples are provided to illustrate the advantages of the proposed approach when compared to other techniques from the literature.