Fault tolerant control for Takagi-Sugeno systems with unmeasurable premise variables by trajectory tracking

Abstract — This paper presents a new method for fault tolerant control of nonlinear systems described by Takagi-Sugeno fuzzy systems with unmeasurable premise variables. The idea is to use a reference model and design a new control law to minimize the state deviation between a healthy reference model and the eventually faulty actual model. This scheme requires the knowledge of the system states and of the occurring faults. These signals are estimated from a Proportional-Integral Observer (PIO) or Proportional-Multi-Integral Observer (PMIO). The fault tolerant control law is designed by using the Lyapunov method to obtain conditions which are given in Linear Matrix Inequality formulation (LMI). Finally, an example is included. Index Terms — Takagi-Sugeno fuzzy systems, state and fault estimation, PI and PMI observers, Lyapunov stability analysis, linear matrix inequality. I