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

Abstract

AbstractNew 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.