Оцінка зваженого рівня впливу обмежених збурень на якість дескрипторних дискретних систем керування

• Дата: 2023
• Автор: Mazko, Alexey
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2023
• Теми: дескрипторна система; допустима система; рiвень гасіння збурень; H∞-керування; ЛМН
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/38
• Назва журналу: Problems of Control and Informatics

In the classical H∞-control theory, the performance measure of continuous systems with zero initial state is the damping level of external (exogenous) disturbances corresponding to the maximal value of the ratio of the -norms for vectors of regulated output of the object and disturbances. In practice, stabilizing control laws in the form of static or dynamic output feedback controllers that minimizing such characteristics of controlled objects ensure the desired quality and high reliability of their functioning in real conditions. In this paper, for a class of linear descriptor (singular) discrete-time control systems, the problems of evaluation and achievement of the generalized performance measure are investigated, the measure characterize the weighted damping level of the bounded external disturbances, as well as the initial disturbances caused by an unknown initial vector. New criteria are established for satisfying the prescribed upper estimate of the specified performance measure, which are reduced to solving the linear matrix inequalities (LMI). The well-known methods for estimating the -norm of the matrix transfer function of a linear descriptor system (statements of the «bounded real lemma» type) follow from the obtained statements for weighted performance measure. When considering the problem of synthesis for a linear descriptor system with regulated and observed outputs, the necessary and sufficient conditions in the form of three matrix inequalities are established for the existence of a static output-feedback controller under which the closed-loop system is admissible (regular, stable and causal) and the desired estimates of the used weighted performance measure are achieved. In terms of LMI, a technique is proposed for constructing an ellipsoidal set of matrices of a static output-feedback controller which provides the closed-loop system with the specified properties. Moreover, the positive definite matrices that define this ellipsoidal set can be both given and sought components of the LMI solution. To illustrate the obtained results and the possibility of numerical implementation of the proposed methods with the help of computer tools, an example of a descriptor control system of an electric circuit is presented.