QUASI-OPTIMAL CONTROL OF ONE CLASS OF SYSTEMS WITH DISTRIBUTED PARAMETERS - Berkimbaeva, С.; Dalbekova, К.; Kadenova, З.; Iskakova, А.; Akkozieva, Р. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2025)
The concept of absolute stability is one of the important phenomena in the study of various processes in reality. Absolute stability of systems with distributed parameters means stable operation of the system under any admissible nonlinearities, which makes it important for practical application. As a consequence, there is a need to study such research methods that would ensure stability in a certain range of changes in the system parameters. Absolute stability of a hybrid system described by hyperbolic partial differential equations can be obtained in the form of a frequency inequality. Since checking the frequency condition in the space of system parameters is a rather complex task, then for its solution it is possible to make a transition from the frequency condition to an algebraic criterion of absolute stability based on the Sturm method applied to quasi-polynomials. This article considers a hybrid system described by hyperbolic partial differential equations. Absolute stability of such a system can be obtained in the form of a frequency inequality, according to the frequency criterion of the V.M. Popov type. But checking the frequency condition in the space of system parameters is a rather complex task. In this regard, the proposed work makes a transition from the frequency condition to the algebraic criterion of absolute stability