A Lyapunov functional for a neutral system with a time-varying delay

Abstract

Abstract. The paper presents a method of determining of the Lyapunov functional for a linear neutral system with an interval time-varying delay. The Lyapunov functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the trajectory of the system with a time-varying delay. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

A Lyapunov functional for a system with both lumped and distributed delay

“…Duda [3] presented that method of determining of the Lyapunov functional for a linear dynamical system with two lumped retarded type time delays in the general case with non-commensurate delays and presented a special case with commensurate delays in which the Lyapunov functional could be determined by solving of the ordinary differential equations set. Duda [4] presented also the method of determining of the Lyapunov functional for a neutral system with k-non-commensurate delays and in [9] for a linear system with both lumped and distributed delay, and in [5] for a system with a time-varying delay.…”

Analysis of Functional and Neutral Differential Equations via Lyapunov Functionals

“…The results of Theorem 6 and Corollary 3 have profound usage in the study of control theory. For example, in [27] the author considered the control system In the papers [6,[11][12][13][14][15] it was argued that if the zero solution of 𝑑𝑦(𝑡) 𝑑𝑡 = 𝑎𝑦(𝑡) is asymptotically stable, then the zero solution of (4.18) is asymptotically stable provided that |𝑎𝑐 + 𝑏| < 1.…”

Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays

“…The method of determination of a Lyapunov functional for a time delay system with one delay, for the first time, was presented by Repin [13]. Duda used the Repin's method to determination of a Lyapunov functional for a system with two delays [2], for a neutral system [3], for a system with a time-varying delay [4,5], for a neutral system with both lumped and distributed delay [7].…”