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Summation Inequalities

In: Dynamic Systems with Time Delays: Stability and Control

Author

Listed:
  • Ju H. Park

    (Yeungnam University, Department of Electrical Engineering)

  • Tae H. Lee

    (Chonbuk National University, Division of Electronic Engineering)

  • Yajuan Liu

    (North China Electric Power University, Control and Computer Engineering)

  • Jun Chen

    (Jiangsu Normal University, School of Electrical Engineering and Automation)

Abstract

This chapter is concerned with the study of summation inequalities as they are widely used in the stability analysis of discrete-time systems with time delays. According to whether free matrices are involved or not, summation inequalitiesSummation inequality are classified into two types: those without free matrices and those with free matrices. Different types of summation inequalities may lead to different ways of estimating summation terms. In this chapter, various summation inequalities are proposed, including some well-known ones such as the Jensen and Wirtinger-based summation inequalities, and several series of summation inequalities with an undetermined parameter N. It is worth pointing out that orthogonal polynomials defined in summation inner spaces play an essential role in achieving summation inequalities.

Suggested Citation

  • Ju H. Park & Tae H. Lee & Yajuan Liu & Jun Chen, 2019. "Summation Inequalities," Springer Books, in: Dynamic Systems with Time Delays: Stability and Control, chapter 0, pages 93-122, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-9254-2_4
    DOI: 10.1007/978-981-13-9254-2_4
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