Stability tests for neutral‐type delay systems: A delay Lyapunov matrix and piecewise linear approximation of the functional argument approach

New necessary and sufficient stability tests for neutral‐type linear time delay systems are presented. They are based on functionals with prescribed derivative depending on the delay Lyapunov matrix and recent stability/instability theorems. A piecewise linear approximation of the initial function a...

Full description

Saved in:
Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 34; no. 9; pp. 5664 - 5685
Main Authors Portilla, Gerson, Alexandrova, Irina V., Mondié, Sabine
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.06.2024
Subjects
Approximation
linear time delay systems of neutral type
Lyapunov matrix
Lyapunov–Krasovskii functionals
Quadratic forms
stability
Stability criteria
Stability tests
Time delay systems
Online AccessGet full text

Cover

More Information
Summary:New necessary and sufficient stability tests for neutral‐type linear time delay systems are presented. They are based on functionals with prescribed derivative depending on the delay Lyapunov matrix and recent stability/instability theorems. A piecewise linear approximation of the initial function argument in the functional is employed. As a result, the functional is approximated via a quadratic form whose matrix provides stability criteria. This matrix involves the integrals based on the delay Lyapunov matrix which are handled via an efficient computational procedure. The main feature of these tests is that they are verified in a finite number of operations, which is achieved through rigorous bounding of the approximation error on a specific class of functions. Some examples which validate the obtained results are presented and discussed.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.7293