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

Abstract

This study 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.