Abstract: The problem of robust H∞control for a class of discretetime singular systems with normbounded uncertainties and delaydependent was investigated. Firstly， based on linear matrix inequality(LMI)， combined with complete theory， by means of the multiple Lyapunov function method， under the appropriate switching rules， a sufficient condition was proposed for the problem to be solvable with all admissible uncertainties state delay; then， based on this condition， a delaydependent sufficient condition was proposed by designing the corresponding subcontrollers， such that the closedloop system was guaranteed robust stable and had H∞performance. Numerical examples show that the method is effective.

Key words: switched systems, singular systems, discretetime systems, robust control, multiple Lyapunov function