New design method on memoryless control for singular systems with delayed state and control using LMI

This note presents a new memoryless H ∞ controller design method for singular systems with delayed state and control by linear matrix inequality (LMI) technique. Since lemma and theorem in the paper by Hung and Lee ( J. Franklin Inst. 336 (1999) 911–923) are incorrect, the errors are pointed out. And then, a new state feedback H ∞ controller design algorithm for singular systems with delayed state and control by LMI approach. All solutions including controller gain can be obtained simultaneously because the presented condition is an LMI regarding all variables.