Stability of State Delay Systems Using a Constant Matrix

Abstract

이 논문에서는 상태방정식에서 상태항에 시간지연이 있는 시스템의 안정성을 다루고 있다. 먼저, 상태 시간지연 시스템의 허축의 근이 어떤 상수 행렬의 고유치가 됨을 보였다. 이 결과를 이용해, 상태지연시간이 구간으로 주어지는 시스템에 대한 안정성의 조건을 유도하였다. 이 안정조건은 상태 시간지연 시스템이 불안해질 때 반드시 허축에 근을 가지는 사실을 이용하였다.

This paper is concerned with stability of state delay systems in which the state delay is known to lie in a certain range. It is shown that if the characteristic equation of a state delay system has pure imaginary roots, then the roots are pure imaginary eigenvalues of a constant matrix. Using this result, a stability condition is proposed through which the stability of state delay systems for all state delays belonging to a known range is guaranteed, The condition is based on the certain fact that the state delay system has pure imaginary roots when the system becomes unstable as the state delay increases.

This paper is concerned with stability of state delay systems in which the state delay is known to lie in a certain range. It is shown that if the characteristic equation of a state delay system has pure imaginary roots, then the roots are pure imaginary eigenvalues of a constant matrix. Using this result, a stability condition is proposed through which the stability of state delay systems for all state delays belonging to a known range is guaranteed, The condition is based on the certain fact that the state delay system has pure imaginary roots when the system becomes unstable as the state delay increases.