Robust stabilization and controller design for delta operator based fuzzy systems with uncertainty

Using delta operator approach, the robust stability analysis and fuzzy control problem for a class of nonlinear systems with parametric uncertainties are studied in a unified framework. The discrete-time Takagi-Sugeno (TS) fuzzy model in delta-operator form is adopted for fuzzy modeling of the uncertain nonlinear system. Then a sufficient condition is derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the TS fuzzy system with parametric uncertainties. The sufficient condition is formulated in terms of linear matrix inequalities and covers both the existing related results for discrete and continuous fuzzy control systems. The robust fuzzy state-feedback controller gains can be directly obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software.