A practical approach to control of nonlinear discrete-time state-delay systems

The robust feedback stabilization of a class of nonlinear discrete-time systems with unknown constant state-delay and uncertain function of nonlinear perturbations is considered based on linear matrix inequality (LMI)-based analysis and design procedures. In both cases of nominal and resilient feedback designs, the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. A dynamic output feedback controller is then designed for this class of systems. Seeking computational convenience, all the developed results are cast in the format of LMIs and several numerical examples are presented throughout the paper to demonstrate the advantages of the design methods.