Abstract
Integral inequalities play an essential role in the stability analysis of continuous-time systems with time delay. So, developing an accurate integral inequality is of particular importance. In this chapter, we will focus on the study of integral inequalities. Various single- and multiple-integral inequalities will be presented, including some existing well-known ones such as the Jensen, Wirtinger-based and free-matrix-based inequalities. All of these inequalities can be classified into two types: those without free matrices and those with free matrices. The relationship between the two corresponding inequalities with and without free matrices is discussed. It is worth pointing out that polynomials, especially, orthogonal polynomials, are usually employed to develop integral inequalities. Moreover, more polynomials considered, tighter bounds produced.
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Park, J., Lee, T.H., Liu, Y., Chen, J. (2019). Integral Inequalities. In: Dynamic Systems with Time Delays: Stability and Control. Springer, Singapore. https://doi.org/10.1007/978-981-13-9254-2_3
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DOI: https://doi.org/10.1007/978-981-13-9254-2_3
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