Remarks on Lyapunov-Krasovskii Functionals with Weak Decay Rates
IEEE International Conference on Control and Automation, ICCA
In the existing Lyapunov literature, the decay rate of a Lyapunov-Krasovskii functional along trajectories is commonly required to be comparable to the norm of the state variables (or output variables) over the delay interval. In this work we consider a class of Lyapunov-Krasovskii functionals whose decay rates along trajectories depend only on the current values of the state or output variables. We show that for one type of input-to-output stability property (which leads to input-to-state stability when the output and the state variables are the same), a Lyapunov-Krasovskii functional with the weaker decay rate will still be sufficient for the corresponding stability property.
Kankanamalage, H., Lin, Y., & Wang, Y. (2019). Remarks on Lyapunov-Krasovskii Functionals with Weak Decay Rates. IEEE International Conference on Control and Automation, ICCA, 21-26. https://doi.org/10.1109/ICCA.2019.8900018