Delay-dependent stochastic finite-time ℓ1-gain filtering for discrete-time positive Markov jump linear systems with time-delay

This paper deals with the stochastic finite-time ℓ1-gain filtering problem for discrete-time positive Markov jump linear systems (MJLSs) with time-delay. By using twice augmentation system approach of the Markovianized system variables and further analyzing the relationship of finite-time boundedness and finite-time ℓ1-gain performance between the positive MJLS with time-delay and the augmented systems, a delay-dependent sufficient condition in the form of linear programming (LP) is established such that the resulting filtering error system is positive, stochastically finite-time bounded and has prescribed finite-time ℓ1-gain performance. Then the design of the stochastic finite-time positive ℓ1-gain filter is converted into solving some LP-based conditions. A numerical example is given to validate the proposed filtering design method.