Abstract
The stability of sampled-data systems is investigated using a new type of Lyapunov functional. The interval from the sampling point t k to t k+1 is assumed to be a sampling interval. By fully utilizing the characteristic information on the whole sampling interval, a new two-sided closed-loop Lyapunov functional is proposed, which utilizes the information on both the intervals from the sampling point t to t k and from t to t k+1 . Based on the two-sided closed-loop Lyapunov functional and modified free-matrix-based inequality, a less conservative stability criterion is derived for a sampled-data control system, and three numerical examples are provided to verify the effectiveness and reduced conservativeness of the proposed method. Furthermore, the proposed method is applied to solve the stability problem of electric power markets, and the practical significance of reducing the conservativeness is discussed.
Highlights
With the rapid development of communication and computer technology, sampled-data control has become a core technology in the field of automatic control
The maximum update period, TmctM, of the acceptable power price signal calculated by the stability criterion, meaning the sampling period in the sampled-data control system can be used as a reference for selecting a sampling device, such as the capacity and type of communication channel, and the sampling frequency of signal collector
This study provides a method for analyzing the stability of sampled-data control systems, and applies it to the electric power market
Summary
With the rapid development of communication and computer technology, sampled-data control has become a core technology in the field of automatic control. The larger the sampling period for a stable system, the lower the conservativeness, and the lower the requirements for communication rate, capacity, and bandwidth of the system. This indicates that the larger the allowed sampling period, the lower the requirements for the system’s hardware, and sampling performance, and in turn, lower the cost of sampleddata control equipment.
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