An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers

This letter investigates the problem of stability analysis and output-feedback stabilization of discrete-time Lur'e systems where the nonlinearity is odd and slope bounded. Using the linear matrix inequality (LMI) conditions from the literature to handle thel1norm and positive realness constraints, an iterative algorithm based on LMIs is constructed to assess stability through the existence of a Zames-Falb multiplier of any given order based on independent positive definite matrices for thel1norm and positive realness. More important, the method can also deal with output-feedback stabilization. Numerical examples illustrate the performance of the proposed approach when compared with other methods.