Observers Design for 2-D Positive Time-Delay Roesser Systems

The problem of designing positive observers for 2-D positive Roesser systems with delays is addressed in this brief. Specifically, the design of an extended Luenberger-type observer that generates a nonnegative asymptotic estimation of the state vector and a reduced-order functional state observer that is an asymptotic approximation of a given linear functional of the state vector is considered for 2-D positive delayed systems. By utilizing the positivity and linear programming (LP) approach, necessary and sufficient delay-independent conditions are first derived for the existence of desired observers. Then, based on the existence conditions, effective design procedures are formulated using the LP setting to obtain the observer parameters. Finally, the efficacy of the design method is demonstrated by two numerical examples.