# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Stability and feedback stabilization of HIV infection model with two classes of target cells. (English) Zbl 1248.93134
Summary: We study the stability and feedback stabilization of the uninfected steady state of a human immunodeficiency virus (HIV) infection model. The model is a 6-dimensional nonlinear ODEs that describes the interaction of the HIV with two classes of target cells, CD4${}^{+}$ T cells and macrophages, and takes into account the Cytotoxic T Lymphocytes (CTLs) immune response. Lyapunov function is constructed to establish the global asymptotic stability of the uninfected steady state of the model. In a control system framework, the HIV infection model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is considered as a nonlinear control system with drug dose as control input. We developed treatment schedules for HIV-infected patients by using Model Predictive Control (MPC-)based method. The MPC is constructed on the basis of an approximate discrete-time model of the HIV infection model. The MPC is applied to the stabilization of the uninfected steady state of the HIV infection model. Besides model inaccuracies that HIV infection model suffers from, some disturbances/uncertainties from different sources may arise in the modelling. In this work the disturbances are modelled in the HIV infection model as additive bounded disturbances. The robustness of the MPC against small model uncertainties or disturbances is also shown.
##### MSC:
 93D15 Stabilization of systems by feedback 92D30 Epidemiology