Linear matrix inequality conditions of nonlinear systems by genetic algorithm-based H_∞ adaptive fuzzy sliding mode controller

In this paper, the stability analysis of a genetic algorithm-based (GA-based) H_∞ adaptive fuzzy sliding model controller (AFSMC) for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving fuzzy logic control (FLC) rules. Then, FLC rules and the consequent parameter are decided on via a genetic algorithm. After this, we guarantee a new H_∞ tracking performance inequality for the control system. The H_∞ tracking problem is characterized to solve an eigenvalue problem. Next, an AFSMC is proposed to stabilize the system so as to achieve good H_∞ control performance. Lyapunov's direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality problem. Finally, a numerical simulation is provided to demonstrate the control methodology.