Discrete‐time control for switched positive systems with application to mitigating viral escape

This paper has been motivated by the problem of viral mutation in HIV infection. Under simplifying assumptions, viral mutation treatment dynamics can be viewed as a positive switched linear system. Using linear co‐positive Lyapunov functions, results for the synthesis of stabilizing, guaranteed performance and optimal control laws for switched linear systems are presented. These results are then applied to a simplified human immunodeficiency viral mutation model. The optimal switching control law is compared with the law obtained through an easily computable guaranteed cost function. Simulation results show the effectiveness of these methods.