새로운 구속된 이차함수 음 조건을 이용한 시간지연 선형 시스템의 개선된 안정성

Abstract

This paper considers the delay-dependent stability of linear systems with a time-varying delay in the frame of the Lyapunov-Krasovskii functional(LKF) approach. First, we choose an LKF that is the form of a constrained quadratic function(CQF) for the delay in its time-derivative and a quadratic integral. Second, the Bessel-Legendre inequality and the reciprocally convex inequality are used to find the upper bound of the quadratic integral. Third, a new form of necessary and sufficient condition is adopted to equivalently transform the CQF into the form of Linear matrix inequality(LMI). Finally, two well-known numerical examples are given to show the usefulness of the proposed result.