Delay-dependent H_∞ control of uncertain discrete delay systems

A delay-dependent solution is given for state-feedback H_∞ control of linear discrete-time systems with unknown constant or time-varying delays and with polytopic or norm-bounded uncertainties. Sufficient conditions are obtained for stability and for achieving design specifications which are based on Lyapunov-Krasovskii functional via a descriptor representation of the system. Similarly to the corresponding continuous-time results these conditions provide an efficient tool for analysis and synthesis of linear systems with time delay. The advantage of the new approach is demonstrated via a simple example.