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

In this paper, the perturbed continuous-time interconnected system with time-delay is represented by an equivalent Takagi-Sugeno type fuzzy model having ri 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 ri fuzzy rules rather than ri×ri rules 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.