Controller Design For Singular Systems With State Delays And Uncertainties

By using LMI techniques and Lyapunov stability theory mainly, the paper discusses the design methods of H_∞controller and positive real controller for uncertain singu- lar systems with state delays respectively.The first part considers H_∞control problem for uncertain continuous singular sys- tems with state delays, and gives sufficient condition such that the systems are general quadratic stable and satisfy some H_∞property. The paper further obtains the design method of non-fragile H_∞controller for such systems in the case of controller gain perturbation, and gains the design method of non-fragile H_∞controller for uncertain singular systems with state delays both in state equation and in output equation. Final- ly, a numerical example is given to illustrate the effectiveness of the proposed method.In the second part, positive real control is studied. The sufficient condition such that discrete singular systems with state delays are ESPR is given; Based on this condition, the design method of positive real controller for uncertain discrete singular systems with state delays is obtained. Then, the paper considers positive control problem for uncertain continuous singular systems with state delays.Finally, the paper points out some problems which should be studied further.