Robust digital control of fuzzy systems with parametric uncertainties: LMI-based digital redesign approach

This paper presents a new intelligent digital redesign (IDR) method for uncertain nonlinear systems which are represented by a Takagi–Sugeno (T–S) fuzzy model. The term IDR involves converting an analog controller into an equivalent digital one in the sense of state-matching. The IDR problem can be reduced to finding the digital fuzzy gains minimizing the norm distance between the closed-loop states of the analog and digital control systems. The uncertainties in the plant dynamics are considered in the IDR condition that plays an important role in the performance improvement. Also, the robust stability is well guaranteed in the proposed IDR procedure. Its constructive conditions are expressed as linear matrix inequalities (LMIs). Two numerical examples, the chaotic Lorenz system and the Qi system, are demonstrated to visualize the feasibility of the proposed methodology.