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 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 . Clearly, for the single-rate case, this switching period is equal to the sampling period . 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.