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 [Formula Omitted]-gain and [Formula Omitted]-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 [Formula Omitted] performance. Second, sufficient conditions for a mixed [Formula Omitted] 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.