Admissibility analysis and robust non-fragile controller construction for uncertain T-S fuzzy descriptor systems

Regarding the stability control problem of uncertain Takagi-Sugeno (T-S) fuzzy descriptor systems, a non-fragile controller design method based on the collaborative scaling of multi-parameter uncertain terms is devised in this paper. First, through the joint scaling of system parameter uncertain terms Δ A and the boundaries of the derivative functions of membership functions, the system stability problem is converted to a problem that can be solved by Linear Matrix Inequalities (LMIs). Moreover, the admissibility of the system is rigorously verified. Second, relying on the analysis results, a non-fragile controller is designed, and a dynamic scaling mechanism for the gain uncertain term Δ K is introduced to mitigate the conservatism of the control system. Finally, simulation validation covers basic uncertain systems, complex scenarios with gain uncertainties, as well as practical systems such as inverted pendulum cart systems and biological population systems. Quantitative comparisons demonstrate that the proposed method ensures asymptotic stability of the system; meanwhile, it outperforms existing approaches in terms of the range of feasible regions, the tolerated limit robust uncertainty threshold, and dynamic response efficiency, providing new ideas for the robust control of non-linear engineering fuzzy systems.