Ruslan S. Ivlev

Institute of Informatics and Control Problems of Ministry of Education and Science of Republic of Kazakhstan

e-mail: ivlevruslan@newmail.ru

In recent years the tasks that are characterized with having of uncertainty in specifying control objects parameters attract researches attention. Such an uncertainty can be caused with reasons of various sorts: measurement errors, a priori inexact information and so on. An uncertainty of this type can be represented as belonging real parameters value to some intervals with specified bounds, and mathematical models of control objects can be represented using rules and terminology of intensively developing interval mathematics. The class of such control objects is called intervally specified.

Historically one of the first paper devoted to investigating intervally specified systems is considered to be Kharitonov paper, which was incentive to further investigation in this field. Despite of a great deal of works having the main purpose to obtain results similar to Kharitonov theorems for the case of investigating some dynamics properties at interval matrices (stability, positive definiteness and so on) this question remains open now. For example, stability of all possible vertex matrices of a given interval one of dimension does not ensure stability of the whole interval matrix. Moreover, recent research showed, the task of obtaining necessary and sufficient conditions of having such properties as stability, positive definiteness, regularity for interval matrices is NP-hard. In the light of the mentioned the task of obtaining new and effective methods of investigating dynamics properties of interval matrices are actual now.

Using Lyapunov approach which has been quite positive succeeded in solving many tasks of control theory for the problem of investigating stability of interval matrices allows considerably enrich the existing arsenal of methods of solving this task.