An adaptive fuzzy control of continuous nonlinear systems

This paper treats the problem of an adaptive fuzzy control of continuous nonlinear systems which contain unknown constant parameters in their state space. These systems are represented by Takagi-Sugeno fuzzy model. The quadratic Lyapunov function is used in the stability analysis and the design of fuzzy controllers. A common symmetric positive definite Lyapunov matrix allows us to determine an update law to estimate the vector of the unknown constant parameters and make the global output of the Takagi-Sugeno fuzzy model track the desired output. The obtained conditions are described by linear matrix inequalities. The case of an unstable continuous nonlinear system of third order is considered to illustrate the proposed approach.