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

Abstract

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

Archives of Control Sciences

“…The Lyapunov functional is determined by means of the Lyapunov matrix. This paper extends the results of Duda [5,6] to a system with two delays and a PD-controller. To the best of the author's knowledge, such extension has not been reported in the literature.…”

“…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.…”

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].…”