Grey Forecast And Robust H_∞Control For Grey Descriptor Time-delay Systems

Because of profound practical background, grey control and grey forecast has aroused widespread concern and achieved fruitful research results.Grey forecast in deformation forecast and PID control are studied, and improved model are given respectively. The robust H∞control problem of grey descriptor time-delay system is studied and robust stability criterions are given.First of all, to the problem that instrument operation and measure error make metrical deformation data away from the fact, wavelets denoise theory is used to filtered noise in metrical data. And the original value of grey self-adaptive model is amended. Then, the improved self-adaptive grey model based on wavelets denoise theory is given. A foundation trench example is given to show that this method is more precise than the normal grey forecast model.And then, modified grey PID control model is given. Grey self-adaptive model is used to replace GM (1,1) model. The recent message and forecast message are used to amend PID model, so control can reach the prospective effect. An air-condition example is used to show validity of this model.Finally, the problems of robust quadratic stability and robust H∞control for grey descriptor system with time-delay are studied. By matrix decomposition method, the grey part is changed into uncertain problem, and robust of descriptor uncertain system with time-delay has been studied. So the problems can be solved. Sufficient conditions for the robust quadratic stability and robust H∞control problem are given. All the results are presented in terms of linear matrix inequality (LMI). A numerical example is provided to demonstrate the validity of the proposed method.