ℒ₁ Control of Positive Semi-Markov Jump Systems With State Delay

In this article, the issue ofL₁control design is addressed for a class of delayed stochastic jump systems subject to semi-Markov jump parameters. The stochastic jump systems in the presence of positivity constraints are described by positive semi-Markov jump systems (S-MJSs). By constructing new linear Lyapunov functional dependent double integral, some sojourn-time-dependent sufficient conditions are established to realize the corresponding stochastic stability with a prescribedL₁-gain performance index. Then, a switching controller via gain matrix decomposition is designed to achieve positivity and stochastic stabilization with a prescribedL₁-gain performance, which can be solved with the help of linear programming approach. Finally, the virus mutation treatment model verifies the effectiveness of the theoretical results.