Nonlinear decentralized state feedback controller for uncertain fuzzy time-delay interconnected systems

摘要

In this paper, the perturbed continuous-time interconnected system with time-delay is represented by an equivalent Takagi-Sugeno type fuzzy model having r_i rules for each subsystem. Based on Lyapunov stability theorem and Razumikhin theorem, the nonlinear decentralized state feedback fuzzy controllers are proposed to stabilize the whole-perturbed fuzzy time-delay interconnected system asymptotically. Under using this nonlinear controller, the design methods only consider the r_i fuzzy rules rather than r_i x r_irules for each subsystem, that is, we can remove the negative effect of the coupled terms. Therefore, these approaches can be less conservative. Moreover, if all the time-delays of each subsystem are the same for all rules, we shall propose less conservative criteria. These criteria do not need the solution of a Lyapunov equation or a Riccati equation. We also do not need to find a common positive matrix P to satisfy any inequality. The so-called "matching condition" for the interconnection matrices and perturbations are not needed. Finally, a numerical example is given to illustrate the control design and its effectiveness.