Passivity and passification for Markov jump genetic regulatory networks with time-varying delays

This paper investigates the problems of passivity and passification for a class of nonlinear Markov jump genetic regulatory networks with time-varying delays and disturbances. By utilizing the Lyapunov–Krasovskii functional method, a novel delay-dependent passivity criterion is established in terms of linear matrix inequalities to guarantee the Markov jump genetic regulatory networks to be passive. Then, based on the obtained passivity conditions, the passification problem is further solved by designing a mode-dependent state feedback controller. A numerical example is presented to demonstrate the effectiveness and validity of the proposed approaches.