ℒ₁ Control of Positive Semi-Markov Jump Systems With State Delay
Guangdeng Zong, Wenhai Qi, Hamid Reza Karimi · IEEE Transactions on Systems Man and Cybernetics Systems · 2020
In this article, the issue of$\mathscr {L}_{1}$control 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 prescribed$\mathscr {L}_{1}$-gain performance index. Then, a switching controller via gain matrix decomposition is designed to achieve positivity and stochastic stabilization with a prescribed$\mathscr {L}_{1}$-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.