Fractional Differential Control System Stability And Controllability With Time Delay

This paper make a research on delay differential control system problems, the stability of fractional order neutral type control system and the controllability prob-lem is main studied, and some valuable results are obtained.The organization structure of full text is divided into four chapters:The first chapter mainly introduces some differential equations historical background, which has realistic cross field of neutral functional differential equations of the problem do-main in the control system do a simple narrative, finally introduces some preliminary knowledge about the fractional calculus.The second chapter considers the stability of neutral fractional differential s-liding mode control system, by construction an appropriate sliding mode surface, finding the equivalent control and switching control, then to achieve the sliding mode system or to approach the sliding surface. Proving the existence by the Lya-punov function, at last, the stability of the control system is established by using the generalized Gronwall inequality.The third chapter discusses the fractional differential control systems, through the solution of a differential system without control, find out the base solution ex-pression, then giving the control system to discuss the solution. Construction Gram matrix, system controllability’s necessary and sufficient conditions is illustrated.The fourth chapter mainly study a kind of the modified minimum control of the fractional order differential control systems, some of the commonly used formula of fractional calculus are deduced. Using inner product method, defines the minimum modification, and the modified minimum control to construct Gram matrix, proving the delay control systems controllability problems.