Robust l1 minimization for linear time-delay systems

In this paper, the problem of persistent bounded disturbance rejection of linear continuous-time systems with time-varying delays is investigated using the tools of invariant set analysis and Lyapunov-function methodology. We derive less conservative sufficient conditions on robust attractor for time-delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired L₁-performance. A robust state-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example.