Improved Criteria for Controllability of Markovian Jump Boolean Control Networks with Time-Varying State Delays

This article studies the controllability of time-varying-delayed Markovian jump Boolean control networks (DMJBCNs). To begin with, a novel augmented approach is proposed to stack the DMJBCNs into expectation form, where the iterative complexity is markedly reduced from $O(N^{\tau +1})$ to $O((\tau +1)N)$ . Under this way, the necessary and sufficient criterion for the fixed-time trajectory controllability of DMJBCNs is derived. Then, constructing another augmented representation for DMJBCNs, the criterion for the finite-time state controllability is presented. Specially, focusing on DMJBCNs with constant delays, by decomposing subsystems and computing the expectation forms piecewise, extra non-augmented criterion for the finite-time state controllability is proposed, where the iterative complexity is further reduced to O(N). Finally, three biological examples are given to illustrate the theoretical results.