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

The focus of this article is to present a sawtooth-characteristic-based free-matrix integral inequality and to discuss its application to sampled-data systems (SDSs). Firstly, the free matrix, which is associated with the sawtooth characteristic of the input delay, is presented and incorporated into the integral inequality. In the development of inequality techniques, this is the first time that a free matrix has been associated with the sawtooth characteristic. On this basis, a corresponding sawtooth-characteristic-based free-matrix integral inequality is established, enabling estimation of the integral quadratic terms of the Lyapunov-Krasovskii functional (LKF) derivative. To overcome the challenges posed by second-order terms resulting from the proposed integral inequality, augmented system variables associated with the sawtooth characteristic are also introduced. Thus, the complicated calculation arising from second-order terms and the conservatism caused by the quadratic estimation of the LKF can be avoided. Finally, through the utilization of the sawtooth-characteristic-based free-matrix integral inequality, stability criteria with less conservatism are derived for the SDSs in the form of linear matrix inequalities. The superiority of the proposed approach is illustrated through two numerical examples and a simplified sampled-data based power market.