On The Study Of Asymptotically Stable For Fractional-order Neutral Retarded Dynamic Systems

The past two decades, we study some practical systematic, such as thermodynamics, visco-elasticity, acoustics, electro-chemical, rheological wich revealed the real nature of physical objects are fractional order. At the same time, the delay will inevitably the presence in various engineering systems, its presence may become unstable and performance deteriorated for the systems, so fractional order systems with time-delay is studied by some scholars. Later, we found that fractional-order neutral delay dynamic system is a more practical system. However, no one to discuss them at present。Thus, this paper carried out in depth for these system. At last, we not olny enrich fractional order differential dynamic systems theory, but also the control approach for time-delay neutral fractional order dynamic systems provides new ideas.The main idea of this paper, through the Laplace transform for the systems gain the characteristic equation. If all the roots of the characteristic equation have negative real parts, then the system is asymptotically stable. Based on the Laplace transform, the paper firstly discusses the asymptotic stability for time-varying delay neutral fractional order systems . some conclusions of the existing literature are improved. As its an application, we deal with synchronization between the compartmental models with fractional order in pharmacokinetics by our theorem and the feedback control method.Next, the paper studies the asymptotic stability and the feedback control stability problem for time-varying delay uncertain fractional-order system by linear matrix inequalities. Some sufficient conditions are gived.Finally, we discuss the asymptotic stability and the feedback control stability problem for uncertain time-varying delay neutral fractional order systems by the same method. Some sufficient conditions are expressed.Moreover, in this paper, using MATLAB/SIMULINK software as a tool to study the stability of the new criterion by a computer simulation to illustrate the effectiveness of the proposed method.