Output Feedback Control of Markovian Switching Boolean Control Networks

In this paper, output feedback control of Markovian switching Boolean control networks (MSBCNs) is investigated via the semi-tensor product of matrices and convex programming. First, by reviewing stability results for Markovian switching Boolean networks, one necessary and sufficient condition for output feedback stabilization of MSBCNs is given, based on which a new equivalent condition for output feedback stabilization of MSBCNs is put forward in the form of a convex programming problem. From one feasible solution to this convex programming problem, the controller gains can be easily designed. Finally, an example about the lac operon in the bacterium Escherichia coil is presented to demonstrate the effectiveness of the obtained results.