A new approach for stabilizing nonlinear systems with time delays

The proportional parallel distributed compensation (PPDC) approach is utilized to stabilize time‐delay systems modeled by Takagi‐Sugeno fuzzy models in this article. Based on the Lyapunov stability analysis, stability conditions concerning asymptotical stability of time‐delay systems are established. The main advantage of the PPDC approach over the parallel distributed compensation (PDC) approach is that fewer adjustable parameters are needed to ensure stability. Moreover, the procedure of finding common matrices P and S is simplified and the number of Lyapunov inequalities is reduced significantly. The entire PPDC design procedure employing linear matrix inequalities (LMIs) is presented. A numerical example of stabilizing a continuous stirred tank reactor (CSTR) is given to illustrate salient features of the new approach. © 2002 Wiley Periodicals, Inc.