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 L1 -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 L1/- performance are derived; finally, sufficient conditions for the existence of a mixed L1/- 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.