Stability Analysis of Uniformly Distributed Delay Systems: A Frequency-Sweeping Approach
This chapter addresses the stability of a class of systems including uniformly distributed delays. Compared with the existing results for systems with point-wise constant delays, this problem involves three new technical issues. In this chapter, these technical issues will be solved mainly within the frequency-sweeping framework which was recently established for systems with point-wise delays. As a consequence, the stability in the whole domain of delay can be studied. Moreover, a unified approach will be proposed: Most of the steps required by the problem can be fulfilled by simply observing the frequency-sweeping curves.
X.-G. Li is supported by National Natural Science Foundation of China (61473065), Fundamental Research Funds for the Central Universities (N160402001), and “Digiteo invites” program of France.
- 5.Henrici, P.: Applied and Computational Complex Analysis. Volume 1: Power Series-Integration-Conformal Mapping-Location of Zeros. Wiley, New York (1974)Google Scholar
- 7.Lee, M.S., Hsu, C.S.: On the \(\tau \)-decomposition method of stability analysis for retarded dynamical systems. SIAM J. Control 7(2), 242–259 (1969)Google Scholar
- 9.Li, X.-G., Niculescu, S.-I., Çela, A., Zhang, L., Li, X.: A frequency-sweeping framework for stability analysis of time-delay systems. 62(8), 3701–3716 (2017)Google Scholar
- 10.Liacu, B., Morărescu, I.-C., Niculescu, S.-I., Andriot, C., Dumur, D., Boucher, P., Colledani, F.: Proportional-derivative (PD) controllers for haptics subject to distributed time-delays: a geometrical approach. In: International Conference on Control, Automation and Systems (2012)Google Scholar
- 16.Zhang, L., Mao, Z.-Z., Li, X.-G., Niculescu, S.-I., Çela, A.: Complete stability for constant-coefficient distributed delay systems: a unified frequency-sweeping approach. In: Chinese Control and Decision Conference (2016)Google Scholar