New stability criteria for Lur'e systems based on vector norms

In this paper, new stability conditions for discrete time Lur'e systems are proposed. Stability tests are achieved using aggregation techniques concept based on the use of vector norms and arrow form systems representation. Explicit stability conditions formulation based on the system instantaneous characteristic polynomial and the state space matrix norm are synthesized. Furthermore, it is shown that the developed solutions extend naturally to several relevant stability results for the introduced class of nonlinear systems. A third order system is considered showing the efficiency of the proposed approaches.