Comments on: "Lyapunov matrices for a class of time delay systems" by V. L. Kharitonov
This correction is important for researchers relying on Kharitonov's approach for stability analysis of time delay systems.
The paper identifies a flaw in Kharitonov's method for constructing Lyapunov matrices for time delay systems, showing that the auxiliary two-point boundary value problem has linearly dependent boundary conditions, thus no unique solution exists.
We prove that an auxiliary two-point boundary value problem presented in V. L. Kharitonov, Lyapunov matrices for a class of time delay systems, Systems & Control Letters 55 (2006) 610-617 has linearly dependent boundary conditions, and consequently a unique solution does not exist. Therefore, the two-point boundary value problem presented therein fails to be a basis for constructing Lyapunov matrices for the class of time delay systems investigated.