Research output: Contribution to journal › Article › peer-review
A Lyapunov Stability Test for Neutral Type Delay Systems: A Discretized Functional Approach. / Portilla, G.; Alexandrova, I.V.; Mondié, S.
In: IEEE Transactions on Automatic Control, Vol. 70, No. 11, 2025, p. 7747-7754.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - A Lyapunov Stability Test for Neutral Type Delay Systems: A Discretized Functional Approach
AU - Portilla, G.
AU - Alexandrova, I.V.
AU - Mondié, S.
N1 - Export Date: 05 February 2026; Cited By: 0; Correspondence Address: S. Mondie; Cinvestav, Department of Automatic Control, 07360, Mexico; email: samondie@cinvestav.mx; CODEN: IETAA
PY - 2025
Y1 - 2025
N2 - Necessary and sufficient stability conditions for neutral type linear time delay systems are presented. Our approach relies on discretizing functionals with prescribed derivatives based on the delay Lyapunov matrix via the discretized Lyapunov functional method introduced in Gu (1997). As a result, the discretized functional is expressed as a quadratic form whose inner block matrix involves the delay Lyapunov matrix valued at discrete points. Remarkably, this matrix is connected with those presented recently in Gomez et al. (2019). This fact, along with the estimation of the functional approximation error on a special set of functions, provides a stability criterion expressed through the positive definiteness of the abovementioned matrix. The use of a simpler structure of the functional, which involves derivatives of the function argument instead of derivatives of the delay Lyapunov matrix, is a key factor to simplify developments. It is worth emphasizing that the discretization of the functional derivative is eliminated thanks to the use of functionals with prescribed derivative. Numerical examples show a considerable reduction of the approximation order required to test stability. © 1963-2012 IEEE.
AB - Necessary and sufficient stability conditions for neutral type linear time delay systems are presented. Our approach relies on discretizing functionals with prescribed derivatives based on the delay Lyapunov matrix via the discretized Lyapunov functional method introduced in Gu (1997). As a result, the discretized functional is expressed as a quadratic form whose inner block matrix involves the delay Lyapunov matrix valued at discrete points. Remarkably, this matrix is connected with those presented recently in Gomez et al. (2019). This fact, along with the estimation of the functional approximation error on a special set of functions, provides a stability criterion expressed through the positive definiteness of the abovementioned matrix. The use of a simpler structure of the functional, which involves derivatives of the function argument instead of derivatives of the delay Lyapunov matrix, is a key factor to simplify developments. It is worth emphasizing that the discretization of the functional derivative is eliminated thanks to the use of functionals with prescribed derivative. Numerical examples show a considerable reduction of the approximation order required to test stability. © 1963-2012 IEEE.
KW - Delay systems
KW - linear systems
KW - neutral type delay systems
KW - stability of linear systems
KW - Convergence of numerical methods
KW - Delay control systems
KW - Linear control systems
KW - Lyapunov functions
KW - Lyapunov methods
KW - Matrix algebra
KW - Timing circuits
KW - Delays system
KW - Functionals
KW - Lyapunov matrix
KW - Lyapunov stability
KW - Neutral type delay system
KW - Neutral-type delay
KW - Stability of linear system
KW - Stability tests
KW - Stability criteria
U2 - 10.1109/TAC.2025.3581132
DO - 10.1109/TAC.2025.3581132
M3 - статья
VL - 70
SP - 7747
EP - 7754
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 11
ER -
ID: 149078128