Lyapunov matrices approach to the parametric optimization of time-delay systems

Abstract

In the paper a Lyapunov matrices approach to the parametric optimization problem of timedelay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.

Lyapunov matrices approach to the parametric optimization of a neutral system

“…In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system is presented. This paper extends the results of Duda [9] to a neutral system.…”

“…Duda [3] used the Repin's method to determination of a Lyapunov functional for a system with two delays, for a system with both lumped and distributed delay [5,10], for a system with time-varying delay [6,8]. In last years a method of determination of a Lyapunov functional by means of Lyapunov matrices is very popular, see for example [9,12,13,14,16].…”

“…The Lyapunov quadratic functionals are also used to calculation of a value of a quadratic performance index of quality in the process of the parametric optimization for time delay systems, see for instance [2,4,7,9]. One constructs a functional for a system with a time delay with a given time derivative whose is equal to the negatively defined quadratic form of a system state.…”

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

“…In last years a method of determination of a Lyapunov functional by means of the Lyapunov matrix is very popular. Duda used this method in parametric optimization problem for a system with one retarded type time delay and a P-controller [6], for a neutral system with one delay and a P-controller [7], for a retarded type time delay system with two delays and P-controller [8] and for a neutral system with two delays and P-controller [10].…”

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

“…Duda used a method of determination of the Lyapunov functional by means of Lyapunov matrix in the parametric optimization problem to a time-delay system with one delay [6] and to a neutral system with one delay [8] . In this paper is presented a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two delays.…”