Time-delays appear in many real processes such as chemical processes, biological systems, transportation systems, digital communication networks, some mechanical systems, etc. Systems with time-delays are called time-delay systems. Controls of time delay systems are more complicated compared to ordinary systems.

Why is it difficult to find stability for linear system with delay?

Frequency domain analysis

frequency

Characteristics of spectrum (pole)

spectrum

How can we find stability for linear system with delay?

Lyapunov stability theorem

lyapunov

Lyapunov-Krasovskii theorem

lyapunov-kra

Related Journal
    • Ko, Jeong Wan, and Poo Gyeon Park. “Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative.” Journal of the Franklin Institute 348.9 (2011): 2674-2688.
    • Park, PooGyeon, Jeong Wan Ko, and Changki Jeong. “Reciprocally convex approach to stability of systems with time-varying delays.” Automatica 47.1 (2011): 235-238.
    • Jeong, Changki, PooGyeon Park, and Sung Hyun Kim. “Improved approach to robust stability and H∞ performance analysis for systems with an interval time-varying delay.” Applied Mathematics and Computation 218.21 (2012): 10533-10541.
    • Lee, Won Il, and PooGyeon Park. “Second-order reciprocally convex approach to stability of systems with interval time-varying delays.” Applied Mathematics and Computation 229 (2014): 245-253.
    • Lee, Won Il, Seok Young Lee, and PooGyeon Park. “Improved criteria on robust stability and H∞ performance for linear systems with interval time-varying delays via new triple integral functionals.” Applied Mathematics and Computation 243 (2014): 570-577.
    • Park, PooGyeon, Won Il Lee, and Seok Young Lee. “Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems.” Journal of the Franklin Institute 352.4 (2015): 1378-1396.
    • Lee, Won Il, Seok Young Lee, and PooGyeon Park. “Improved stability criteria for recurrent neural networks with interval time-varying delays via new Lyapunov functionals.” Neurocomputing 155 (2015): 128-134.