Robust ℋ∞ control of uncertain linear time-delay systems: a linear matrix inequality approach. I

This paper is concerned with the robust ℋ_∞ control problem of uncertain linear time-delay systems using a linear matrix inequality approach. The uncertainty described in this paper is in the quadratic constraint form, which takes some well-known uncertainty descriptions as special examples. Four specific problems are tackled, namely the robust ℋ_∞ analysis problem, the robust ℋ_∞ control problem using memoryless static state feedback, the robust ℋ_∞ control problem using memoryless dynamic state feedback and the ℋ_∞ control using memoryless static output feedback. We show that feasibility of some LMIs guarantees the solvability of the corresponding problem