Robust passive control for discrete-time T-S fuzzy systems

Robust stability analysis and passivity for discrete-time Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties was studied via Lyapunov stability theory. Under the assumption of norm bounded parametric uncertainty, the T-S fuzzy model can approximate nonlinear uncertain systems at any precision. On the basis of Lyapunov stability theory, a sufficient condition on the existence of robust passive controllers was derived. With linear matrix inequality (LMI) method, robust passive controllers were designed such that for all admissible uncertainties the closed-loop system is robust stable and strictly passive. The robust passive controller design was parameterized in term of LMI problem. Furthermore, a convex optimization problem with LMI constrains was formulated to design robust passive controllers at maximum dissipation rate. A numerical example demonstrates the effect of the proposed design method.