TY - JOUR

T1 - Lyapunov matrices for a class of time-delay systems with piecewise-constant kernel

AU - Aliseyko, A. N.

PY - 2019/6/3

Y1 - 2019/6/3

N2 - In this contribution, we study time-delay systems with distributed delay whose kernel is piecewise constant. It is shown that the problem of finding a Lyapunov matrix for this class of time-delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions. The problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations. It is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique Lyapunov matrix.

AB - In this contribution, we study time-delay systems with distributed delay whose kernel is piecewise constant. It is shown that the problem of finding a Lyapunov matrix for this class of time-delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions. The problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations. It is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique Lyapunov matrix.

KW - Lyapunov matrix

KW - Lyapunov–Krasovskii functional

KW - time-delay system

KW - Lyapunov-Krasovskii functional

UR - http://www.scopus.com/inward/record.url?scp=85034214924&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/lyapunov-matrices-class-timedelay-systems-piecewiseconstant-kernel

U2 - 10.1080/00207179.2017.1390261

DO - 10.1080/00207179.2017.1390261

M3 - Article

AN - SCOPUS:85034214924

VL - 92

SP - 1298

EP - 1305

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 6

ER -