Positive Filter Design for Positive Markov Jump Linear Systems with Time-Delay, Unknown Disturbance Input and Measurement Noise

This paper proposes some positive filter design results for a class of positive discrete-time delayed Markov jump linear systems against unknown disturbance input and measurement noise in the l1-gain performance sense. Based on the measurement output with noise, a positive delay-dependent and mode-dependent filter is presented. Resorting to the existing necessary and sufficient conditions of stochastic l1-gain performance, some sufficient conditions of positive filter design and a design optimization method are established by the forms of linear programming. Compared with the existing filter design results, the main contributions of the proposed results lie at two aspects: the effect of time-delay on filtering performance is considered and the positivity of the augmented filtering error system can be ensured for the cases that disturbance input and measurement noise are different, and particularly there is no measurement noise. Finally, a numerical example is given to show the design validity.