An Improved Result on Exponential Stabilization of Sampled-Data Fuzzy Systems

This brief paper studies the exponential stabilization problem for the Takagi–Sugeno fuzzy systems with a variable sampling. Different from previous results, the gains of fuzzy state feedback controller adopted in this paper are time-varying during two consecutive sampling instants, which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter. To reduce the design conservativeness, a novel fuzzy time-dependent Lyapunov functional (FTDLF) is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions. Moreover, a more relaxed constraint condition is presented to ensure the positive definiteness of the FTDLF on sampling intervals. By resorting to the novel FTDLF and the relaxed constraint condition, new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established, by which a larger sampling interval can be achieved. One example is offered to demonstrate the validity and superiorities of the obtained new results.