Stability Analysis of Sampled-Data Systems Based on Sawtooth-Characteristic-Based Hierarchical Integral Inequality

Area of Science:

• Control Engineering
• Systems Theory
• Applied Mathematics

Background:

• Sampled-data systems (SDSs) are crucial in modern control applications.
• Input delays and sampling periods significantly impact SDS stability.
• Existing stability analysis methods for SDSs can be conservative.

Purpose of the Study:

• To develop a new stability analysis method for SDSs with input delays.
• To derive a stability criterion for SDSs using a novel integral inequality.
• To determine the maximum allowable sampling period for stable SDSs.

Main Methods:

• Introduction of a sawtooth-characteristic-based hierarchical integral inequality (SCBHII).
• Development of a high-order two-sided looped-functional incorporating sampling multi-integral states and sawtooth patterns.
• Augmentation of system variables with sawtooth pattern-related terms.
• Formulation of stability conditions using linear matrix inequalities (LMIs).

Main Results:

• The proposed SCBHII enhances accuracy with increasing hierarchy.
• A stability criterion for SDSs with reduced conservatism is achieved.
• The method effectively handles high-order terms without secondary processing.
• Effectiveness demonstrated through numerical examples and a power market model.

Conclusions:

• The SCBHII and associated stability criterion offer a less conservative approach to SDS stability analysis.
• The proposed method provides a robust tool for determining maximum sampling periods.
• This research contributes to the reliable design and implementation of SDSs.