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New design method on memoryless ${H}_{\infty }$ control for singular systems with delayed state and control using LMI. (English) Zbl 1063.93017
Summary: This note presents a new memoryless ${H}_{\infty }$ controller design method for singular systems with delayed state and control by the linear matrix inequality (LMI) technique. Since lemma and theorem in the paper by S.-S. Hung and T.-T. Lee [J. Franklin Inst. 336, 911–923 (1999; Zbl 0979.93031)] are incorrect, the errors are pointed out. And then we present the new state feedback ${H}_{\infty }$ controller design algorithm for singular systems with delayed state and control by the LMI approach. All solutions including controller gain can be obtained simultaneously because the presented condition is an LMI regarding all variables.
##### MSC:
 93B36 ${H}^{\infty }$-control 34A09 Implicit equations, differential-algebraic equations 93C23 Systems governed by functional-differential equations 15A39 Linear inequalities of matrices 93B51 Design techniques in systems theory