An augmented system approach for LMI-based control design of constrained Takagi-Sugeno fuzzy systems

In this paper, we address the control design of a class of constrained Takagi-Sugeno fuzzy systems. These systems are subject to both control input and state constraints. Sufficient design conditions are derived via a judicious use of an equivalent augmentation form of the closed-loop system together with a new parameter-dependent Lyapunov function. The control input nonlinearity is dealt with via a generalized sector condition. These instrumental control tools allow reducing significantly the conservatism of the results while keeping a simple control structure with a low level of numerical complexity. In particular, it has been shown that in many cases the new method can provide better results (in terms of conservatism reduction) than some recent works developed in non-quadratic Lyapunov framework. Several numerical examples are given to illustrate the effectiveness of the proposed method.