Fuzzy control with relaxed nonquadratic stability conditions for inverted pendulum robot system with multiplicative noise

This paper presents the relaxed nonquadratic stabilization conditions for designing fuzzy controller of inverted pendulum robot system via Takagi-Sugeno (T-S) stochastic fuzzy models. With the movable supportive base, the inverted pendulum robot system is applied to simulate human stance. Besides, the stochastic behavior of concerned system is also considered in this paper for investigating the real environment. As mentioned above, the T-S fuzzy model is used to simulate nonlinear inverted pendulum robot system. And, the multiplicative noise term is introduced in the consequent part of fuzzy system. In order to extend the application of this paper, the nonquadratic relaxed technique is employed to develop the stability conditions for finding the feasible solutions. Finally, simulation results are given to demonstrate the usefulness and applicability of the proposed fuzzy controller design approach.