Abstract
This paper investigates the mean stability and stabilisation problem for a class of discrete-time positive Markov jump linear systems where the Mode Transition Probability Matrix (MTPM) is a stochastic process instead of time invariant. By assuming the jump of system mode is governed by a low-layer Markov chain and the variation of corresponding MTPM is governed by a high-layer one, a non-homogeneous positive Markov jump linear system model with two Markov chains is then proposed. Based on this, the necessary and sufficient conditions of mean stability for this concerned model are addressed via analysing the time evolution of the first-order moment of state variables. Second, a mode-MTPM-dependent state feedback controller can then be designed according to the given stability conditions which is solvable in terms of linear programming problems. Finally, a numerical example is provided to show the effectiveness of the presented control strategy.
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