Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays

The dynamic output feedback guaranteed cost control problem is investigated for a class of uncertain discrete-time systems with multiple time-varying state delays and norm-bounded parameter uncertainties. Attention is focused on the design of the dynamic output feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Delay-dependent sufficient conditions for the existence of the desired guaranteed cost controllers are derived without involving model transformation and bounding technique for cross terms, and these conditions are formulated in terms of nonlinear matrix inequalities. An iterative algorithm involving convex optimisations is presented to solve these nonlinear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.