Sampled-data H−/H∞H−/H∞ fault detection and isolation for nonlinear systems in T–S form: An approximate model approach

A direct discrete-time design methodology for the sampled-data fault detection and isolation (FDI) problem is proposed for a nonlinear system in Takagi–Sugeno form. The generalized observer scheme is adopted, accompanied by a bank of the sensors' number of observers. A sufficient condition to find observer and residual gains, based on an accessible approximate—rather than unavailable exact—discrete-time model is proposed in terms of matrix inequalities so that it exhibits H−/H∞H−/H∞ performance and asymptotic stability. An algorithm involving a convex optimization is presented using the cone complementary linearization technique. We show that the FDI observer ensures (modified) H−/H∞H−/H∞ performance and Lagrange stability, when it is connected to the actual nonlinear system.