H∞ control for discrete-time Takagi-Sugeno fuzzy systems

We consider the design problem of H-infinity controllers for discrete-time fuzzy systems. We introduce two Riccati inequalities from the standard H-infinity theory, one for the state feedback controller, the other for the filter gain. We rewrite the second inequality and obtain an equivalent inequality for the inverse. We then rewrite this using LMI to obtain the final form of the inequality and show that the proposed output feedback controller is gamma-suboptimal. We give two examples and construct -y-suboptimal controllers for them.