Positive observer design for discrete-time positive system with missing data in output

This paper is concerned with the positive observer design for a class of discrete-time positive systems with missing data in output. Such a process of missing data is described by a discrete-time Markov chain with two modes. Firstly, a necessary and sufficient condition is proposed to check the positivity of the modeled system. Then, necessary and sufficient conditions depending on some probabilities are developed such that the error system is asymptotically mean stable. Based on the given results, sufficient conditions for the existence of the desired positive observer are provided. Moreover, the obtained results are extended to more general cases that the transition probabilities are uncertain and totally unknown. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods.