Mixed L₁/L_-Fault Detection Observer for Continuous 2-D Positive Systems

This brief concerns the design of a fault detection observer for positive two-dimensional (2D) continuous systems. First, an approach is provided to calculate accurate values of the L1-gain and L-index for positive 2D systems, indicating the robustness and fault sensitivity, respectively. Necessary and sufficient conditions are developed such that the positive 2D systems are asymptotically stable with the L1/L- performance. Second, sufficient conditions for a mixed L1/L- observer are established. An iterative algorithm is formulated to address the multiobjective optimization problem. Finally, the validity and feasibility of the proposed design approach and algorithm are illustrated using a numerical example.