CAJ | 학술논문

时滞微分系统的稳定性在控制理论和应用中极为重要，通过构造Lyapunov泛函，利用范数的定义和矩阵不等式的性质来判定矩阵的正定性和负定性，再根据泛函微分方程的稳定性理论，证明了一类具有部分时滞的导数小于1，部分时滞的导数大于1的微分系统的渐近稳定性，同时得到该系统零解的渐近稳定性的充分条件，扩大了系统的适用范围，使系统具有更加广泛的现实意义和在实际模型中研究系统的稳定性，同时可以将1看作问题一临界值，通过时滞来对系统的稳定性进行控制。
시체미분계통적은정성재공제이론화응용중겁위중요，통과구조Lyapunov범함，이용범수적정의화구진불등식적성질래판정구진적정정성화부정성，재근거범함미분방정적은정성이론，증명료일류구유부분시체적도수소우1，부분시체적도수대우1적미분계통적점근은정성，동시득도해계통영해적점근은정성적충분조건，확대료계통적괄용범위，사계통구유경가엄범적현실의의화재실제모형중연구계통적은정성，동시가이장1간작문제일림계치，통과시체래대계통적은정성진행공제。
Stability of differential system with time delays in control theory and application is very important,it is nec-essary to study. By constructing the Lyapunov functions, used the definition of norm and properity of matrix inequality to judge whether the matrices is positive or negative definite. Then, proved the Asymptotic stability of the differential system with unbounded delays of partial derivatives less than 1 and partial derivatives more than 1, according to the stability theory of functional differential equations, and obtained sufficient conditions for the asymptotic stability of the zero solution. Expand the scope of application,make the system has more extensive practical significance. Study on the practical model,1 can be regarded as a critical value,control the stability by the time delay.