Evolutionary design of static output feedback controller for Takagi–Sugeno fuzzy systems

The design of a static output feedback fuzzy controller for nonlinear systems based on Takagi–Sugeno (T–S) fuzzy models is addressed. To avoid complex mathematical derivations and conservative results, a genetic algorithm (GA) is integrated with a linear matrix inequality (LMI) optimisation to seek the static output feedback gains that satisfy the Lyapunov stability inequalities with a decay rate constraint. To do so, the fitness function of the GA must be made up of constraints that are derived from some fundamental control theories, the Lyapunov stability criteria and LMI solver. To improve the computational efficiency of the GA and LMI solver, a fitness function, called the hierarchical fitness function structure, is built on a hierarchical structure such that the GA can in turn deal with stability inequalities. The relaxed syntheses of static output feedback fuzzy control are then easy to implement without using complex mathematical derivations.