D-stability-based state and actuator fault estimation for Takagi-Sugeno systems with Immeasurable Premise Variables

This paper focuses on state and actuator fault estimation for Takagi-Sugeno systems with Immeasurable Premise Variables (IPV) under D-stability constraints and ${{\mathcal{L}}_2}$-gain analysis. This is achieved through the synthesis of a Fault Adaptive Multiple Observer (FAMO). D-stability is ensured by placing the eigenvalues of the matrices that characterize the dynamics of state and fault estimation errors within a predefined LMI region in the complex plane. The ${{\mathcal{L}}_2}$-gain analysis aims to minimize the effect of immeasurable premise variables. To this end, we propose sufficient and generic LMI constraints to compute the FAMO parameters. Finally, a simulation example demonstrates the validity of the proposed approach.