The HIV infection linearized model developed in Problem 84, Chapter 4, can be shown to have the transfer function

It is desired to develop a policy for drug delivery to maintain the virus count at prescribed levels. For the purpose of obtaining an appropriate u₁(t); feedback will be used as shown in Figure P6.17 (Craig, 2004). As a first approach, consider G(s) = K; a constant to be selected. Use the Routh-Hurwitz criteria to find the range of K for which the system is closed-loop stable.

Data from  Problem 84,Chapter 4:

We developed a linearized state-space model of HIV infection. The model assumed that two different drugs were used to combat the spread of the HIV virus. Since this book focuses on single-input, single output systems, only one of the two drugs will be considered. We will assume that only RTIs are used as an input. Thus, in the equations of Chapter 3, Problem 31, u₂ = 0 (Craig, 2004).

Show that when using only RTIs in the linearized system of Problem 31, Chapter 3, and substituting the typical parameter values given in the table of Problem 31c, Chapter 3, the resulting state-space representation for the system is given by

Y(s) P(s) = U1(s) s3 +2.6817s + 0.11s+0.0126 -520s 10.3844 Desired virus Virus count change, Y(s) P(s) count change U(s) G(s) FIGURE P6.17