Robust Nash Strategy for Uncertain SIR Time-Delay Model

In this paper, a robust Nash strategy for uncertain susceptible-infected-recovered (SIR) model with state delay is investigated. After linearizing the original nonlinear SIR model, a sufficient condition for the existence of a proposed strategy set in terms of full state information is derived in terms of bilinear matrix inequality (BMI). Since the concept is based on the guaranteed cost control technique, robust stability is attained. In order to avoid the treatment of BMIs, a recursive algorithm based on the linear matrix inequality (LMI) is discussed. Finally, a practical SIR time-delay model is demonstrated to show the effectiveness and reliability of the proposed strategy.