Stabilization via extended nonquadratic boundedness for constrained nonlinear systems in Takagi–Sugenoʹs form

This paper studies stabilization of the Takagi–Sugeno fuzzy system with input and state constraints and bounded noise. The technique of extended nonquadratic boundedness is proposed based on the existing quadratic boundedness. Under the non-parallel distributed compensation law, the state of the closed-loop system is stabilizing to a neighborhood of the origin specified via an extended nonquadratic Lyapunov function. The existing technique for relaxing the linear matrix inequality conditions can be properly applied to obtain computationally tractable stability conditions. A simulation example is given to show the effectiveness of the controller.