The Design Of Controller Of Fractional Systems Based On The Indirected Lyapunov Method

Fractional differential equations arise in many engineering and scientific disci-plines as the mathematical modeling of systems and processes in the fields of physics,chemistry,aerodynamics,electrodynamics of complex medium or polymer rheolo-gy[1].On this kind of equations the derivatives of fractional order are involved.The interest of the study of fractional-order differential equations lies in the fact that fractional-order models are more accurate than integer-order models,that is,there are more degrees of freedom in the fractional-order models.Furthermore,fraction-al derivatives provide an excellent instrument for the description of memory and hereditary properties of various materials and processes due to the existence of a“memory”term in a model.This memory term insures the history and its impact to the present and future.In consequence,the subject of fractional differential e-quations is gaining much importance and attention.For details,and the references therein.Integral boundary conditions have various applications in applied fields such as blood flow problems,chemical engineering,thermo-elasticity,underground water flow,population dynamics,and so forth.In the same time,the development and the maturation of the control filed accelerate the fractonal models to permeate more and more fields.Also,the facts motivate the researchers to contribute more and more energy.In fact,the integer models can't satisfy the modern technology and the fractional model can easily be up to it.For example,we can't use the integer ones to characterize the complex system in the nature and society and instead,the fractional system,as the extending of the integer ones,can be more accurate and exact in the description of the real system.In addition,fractional model relatively is an open system,which do good to the researchers discuss and probe the topic more deeply.Hence the design of the fractional control and regulator become the heat of researches.Since the fractional controller hold the excellent property when it comes to the integer ones.According to the requirement the control theory research development,we probe twofold of the the fractional system,which is the research topics and the tool to the research and the main contributions is the followings:(1)Chapter2 research the controller of the fractional-order systems with dis-turbances.Firstly,we consider the nonlinear of the system.With the maturing and the advancing of science and technology,the linear system becomes the classical the-ory and we need to attach importance to the nonlinear ones,which is an inevitable topics.Secondly,it is not easy to get the state of fractional system because the complexity of the system and we can't get the real state of it,then we obtain the similar state by the observation.We simplify the calculation and obtain the sat-isfied results.More imperatively,we can extend the application to the non-fragile controller.(2)In chapter 3,we probe the H? dynamic state-feedback controls of fractional-order systems with disturbances.Even though it is difficult to get the state of the fractional system,we can construct the dynamic state-feedback controller to deal with it,and get the LMIs.In the same time,we prove the accuracy of the results and the ingenious of the method by some example,which is calculated by the Yalmip.(3)Based on the chapter 2,we design the H? observer-based non-fragile for the original system and luckily,the result we get is better tha before.