Abstract—Human Immunodeficiency Virus (HIV) is a type of virus which attacks CD4⁺T cells. Insufficient numbers of CD4⁺ T cells will affect the performance of immunity systems so that someone become riskier to have AIDS or other diseases. HIV phenomenon is modelled as nonlinear system with disturbance, but there is no exact method to solve problems that related with analyzing nonlinear systems with control treatment. Thus, the nonlinear system is approximated into a bilinear system by using Carleman bilinearization method. A robust H_∞ -controller is designed as a control input to accomodate the disturbances in the dynamic system. Generally, the treatment for HIV is merely to obstruct the replication process. Therefore, the robust control input is described as the chemotherapy of hypothetical drugs which aimed to clear off the HIV concentration in blood plasma. Robust H_∞ -control is designed with the coefficient matrix of the bilinear system. The simulation result is analyzed by comparing the effect of the robust control toward bilinear and nonlinear system. From numerical simulations, an individual will experience heavy symptom if the hypothetical drugs chemotherapy is not given. This finding is strengthening the urgency of robust control as a chemotherapy with a waiting time. Based on the numerical simulation with robust H_∞ -control input, bilinear system has trends that give similar interpretation with the trends of nonlinear system. Besides that, robust H_∞ -control on bilinear system has demolishing speed of HIV concentration and infected CD4⁺T cells concentration which approximately equal to the demolishing speed from nonlinear system. Therefore, we can conclude that the performances of H_∞ -control on bilinear system is nearly same as the performances of nonlinear system.

Index Terms—Human immunodeficiency virus, chemotherapy, bilinear systems, carleman bilinearization, robust H_∞ -control.

The authors are with Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia (email: roberd@math.itb.ac.id).

Cite: Jonathan Saputra, Roberd Saragih, Dewi Handayani, "Bilinear Robust H_∞ Controller to Minimize HIV Concentration in Blood Plasma," International Journal of Applied Physics and Mathematics vol. 10, no. 2, pp. 57-64, 2020.

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