Output feedback H∞ control for a class of uncertain nonlinear discrete-time delay systems

In this paper, a linear matrix inequality (LMI)-based approach is presented to design robust output feedback H_∞controllers for a class of nonlinear discrete-time systems with delays and parametric uncertainties. Both the time delays and the uncertainties concerned exist not only in the state, but in the input and measurement output. Firstly, some LMI-based criteria in the form of the GBRL (Generalized Bounded Real Lemma) are provided as useful techniques for both stability analysis and controller synthesis. Next an LMI-based approach is proposed to design dynamic output feedback H_∞controllers for delay systems without parametric uncertainties, but with nonlinearity as well as time delays in the state, the input and the output, which generalizes some previous results for control problems of delay systems. Finally, the results are extended to discrete-time delay systems with uncertainties in linear fractional form in all system matrices. Solvability of the robust control problem for uncertain delay systems can also be reduced to the solutions of LMIs. Illustrative examples are provided to demonstrate the efficiency of our approach.