Lyapunov matrices approach to the parametric optimization of a neutral system

Abstract

In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system 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 neutral system. The Lyapunov functional is determined by means of the Lyapunov matrix.

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].…”

Archives of Control Sciences

“…a system with one retarded type time delay and a P-controller [2], for a neutral system with one delay and a P-controller [4], for a system with two delays and a P-controller [5] and for a neutral system with two delays and a P-controller [6]. In the paper the parametric optimization problem for a linear system with two delays and a PD-controller is presented.…”

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.…”