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

The aim of this article is to investigate the stability of sampled-data systems (SDSs) by introducing a sawtooth-characteristic-based hierarchical integral inequality (SCBHII) and to obtain the maximum allowable sampling period that maintains the stability of the system. First, by associating the sawtooth characteristics of the input delay in SDSs with free matrices, an SCBHII is proposed; its accuracy improves as the hierarchy increases. Subsequently, a high-order two-sided looped-functional, which considers both the sampling multi-integral states and the sawtooth pattern, is introduced to cater to the aforementioned inequality. In addition, the system variables are augmented by sawtooth pattern-related terms, which eliminates the need for additional secondary processing when determining the negative-definiteness of derivatives with high-order terms. By combining the high-order two-sided looped-functional with the proposed SCBHII, a stability criterion for SDSs with reduced conservatism is achieved, presented in the form of linear matrix inequalities. The proposed inequality technique and the stability criterion are shown to be effective and superior through three numerical examples and a real-world simplified power market model.