Sawtooth-characteristic-based free matrix integral inequality and its application to sampled-data systems

Area of Science:

• Control Theory
• Systems Engineering
• Mathematical Analysis

Background:

• Sampled-data systems (SDSs) present unique challenges in stability analysis due to discrete-time sampling.
• Existing integral inequality techniques often lead to conservatism and complex calculations, particularly with input delays.

Purpose of the Study:

• To develop a new free-matrix integral inequality specifically tailored for the sawtooth characteristic of input delays in SDSs.
• To apply this novel inequality to derive less conservative stability criteria for SDSs.

Main Methods:

• Introduction of a novel free matrix associated with the sawtooth characteristic of input delay.
• Development of a sawtooth-characteristic-based free-matrix integral inequality for estimating Lyapunov-Krasovskii functional (LKF) derivative terms.
• Augmentation of system variables to manage second-order terms and reduce LKF quadratic estimation conservatism.

Main Results:

• Establishment of a new integral inequality technique incorporating a free matrix with sawtooth characteristics.
• Derivation of stability criteria for SDSs in the form of linear matrix inequalities (LMIs).
• Demonstration of reduced conservatism and improved computational efficiency compared to existing methods.

Conclusions:

• The proposed sawtooth-characteristic-based free-matrix integral inequality offers a more effective approach to stability analysis of SDSs.
• The method successfully mitigates conservatism and computational complexity, outperforming traditional techniques.
• Validation through numerical examples and a power market application confirms the approach's practical utility and superiority.