Exponentially Almost Sure Stability of Dual Switching Discrete-time Linear Positive System

Dual Switching Discrete-time Linear Positive System (DSDLPS), which subjects simultaneously to deterministic switching mechanisms and stochastic Markov switching mechanisms commutation, is a class of switched system that is switched among finite Markov Switching Discrete-time Linear Positive Systems (MSDLPS), that is, Markov Switching Discrete-time Linear Positive System with non-negative state variables. Meanwhile, the transition probability of the Markov chain is not fixed and is determined by the current position of deterministic switching. In this paper, we address the exponentially almost sure stability problem for DSDLPS. By using stochastic multiple linear co-positive Lyapunov function and the transient analysis of Markov chains, a sufficient condition for the exponentially almost sure stability of DSDLPS under the per-designed deterministic switching strategy is presented. It is remarkable that, owing to the positive system, the sufficient conditions for the exponentially almost sure stability of DSDLPS are solvable in terms of linear programming. Finally, a numerical example is given to illustrate the effectiveness of our results.