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) H1 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 H1 tracking performance inequality for the control system. The H1 tracking problem is characterized to solve an eigenvalue problem. Next, an AFSMC is proposed to sta-bilize the system so as to achieve good H1 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