Multirate robust digital control for fuzzy systems with periodic Lyapunov function

Sampled-data control which is capable of stabilizing general nonlinear systems is of great current interest. In this paper, the Takagi-Sugeno (TS) fuzzy model is used to represent the nonlinear plant. The paper is primarily concerned with designing digital controllers for the TS fuzzy continuous-time model to stabilize the closed-loop system. In the problem formulation, we only assume that the sampled values at a sampling rate of (1/T/sub s/) are available for control. Within the sampling intervals, the fuzzy controller uses the sampled data at the sampling instants to fire a fuzzy rule and generate a digital control action series. This digital control action is then fed into the nonlinear system through a zero-order-holder. In this paper, two kinds of digital controllers are designed: Multirate and single-rate digital controllers. Within a sampling interval, the single-rate controller is static, while the multirate controller is periodically time-varying, i.e., the control action is switched at a small switching period T. Clearly, for the single-rate case, this switching period T is equal to the sampling period T/sub s/. This paper presents a design procedure for the multirate fuzzy controller with the single-rate control as a special case. The results are formulated as linear matrix inequalities. Numerical example shows the effectiveness of the proposed design procedures.