Asymptotic Stability Analysis of Particular Classes of Linear Time-Delay Systems: A New Approach
Dragutin Debeljković,
Sreten Stojanović
This paper
offers new, necessary and sufficient conditions for the delay-dependent
asymptotic stability of systems of the form
and
.
The time-dependent criteria are derived by Lyapunov’s direct method. Two
matrix equations have been derived: matrix polynomial equation and
continuous (discrete) Lyapunov matrix equation. Also, modifications of the
existing sufficient conditions of convergence of Traub and Bernoilli
algorithms for computing the dominant solvent of the matrix
polynomial equation are derived. These results have been extended to large
scale systems as well. Numerical computations are performed to illustrate
the results obtained.