L1/L- Observer-Based Fault Detection for 2-D Delayed Positive Continuous-Time Systems

This brief focuses on the design of fault detection observer for continuous 2D delayed positive systems. Firstly, the L_{1} -gain and L_{-} -index of the 2D positive delayed systems are calculated by 2D Laplace transform; secondly, necessary and sufficient conditions for the system to satisfy the L_{1}/L_{-} performance are derived; finally, sufficient conditions for the existence of a mixed L_{1}/L_{-} observer are derived. The solution to the observer gain is given by an iterative linear programming algorithm. An example is given to demonstrate the validity of the proposed theoretical results.