Positive observers for positive interval linear discrete-time delay systems

Abstract

Linear matrix inequalities (LMIs) provide a powerful analysis and synthesis framework for linear systems. In this paper, we use LMIs to develop positive observers for positive linear discrete-time (PLDT) systems with both parameter uncertainties and time delay. Specifically, we first present some equivalent conditions for the asymptotic stability of positive linear discrete-time delay systems, which will be employed to design the positive observers. Then, necessary and sufficient conditions are proposed to check the existence of positive observers for interval PLDT systems with time delay when the positivity of the error signals is considered, and the observer matrices to be constructed can be easily obtained through the solutions of LMIs. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.