Abstract
This chapter deals with the stability analysis of linear time-delay systems without and with parametric uncertainties. The stability analysis for both constant and time-varying delay in the states is considered. The focus of this chapter is to review the existing methods on delay-dependent stability analysis in an LMI framework based on Lyapunov-Krasovskii approach and consequently the improved results on delay-dependent stability analysis are presented. The results of the proposed techniques are validated by considering numerical examples and compared with existing results.
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Notes
- 1.
\(A(t)=A+\Delta A(t)\), where, \(\Delta A(t)=D_{a}F_{a}(t)E_{a}\).
- 2.
\(A_{d}(t)=A+\Delta A_{d}(t)\), where, \(\Delta A_{d}(t)=D_{d}F_{d}(t)E_{d}\).
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Dey, R., Ray, G., Balas, V.E. (2018). Stability Analysis of Time-Delay Systems. In: Stability and Stabilization of Linear and Fuzzy Time-Delay Systems. Intelligent Systems Reference Library, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-70149-3_2
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DOI: https://doi.org/10.1007/978-3-319-70149-3_2
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