Abstract
This paper examines the problem of designing a nonlinear state feedback controller (SFC) for Takagi–Sugeno discrete-time parametric uncertain systems via an iterative linear matrix inequalities (LMIs). The objective of this paper is to establish a novel framework of the SFC with conservatism reduction (less restrictive) results by introducing slack variables. These reduced conservative results are demonstrated by a larger feasible areas of stabilization (stabilization domain). Nevertheless, this paper shows that by changing the initial nonquadratic Lyapunov function, a better solution can be reached (less restrictive results). By using simulations, we verify the new condition robustness and a comparison with another approach existing in the literature to demonstrate the effectiveness of this new approach.
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