Dissipative Control For Fractional-Order Systems With Time Delay

With the development of the theory for fractional order calculus,scholars have found that fractional order calculus have satisfactory memory abilities and hereditary properties,it makes the fractional order differential systems more accurately describe the dynamical behaviors than the traditional integer order differential systems.In actual engineering,the phenomenon of time delay is inevitable,so it is necessary to study fractional order differential system with time delay in this paper.In this paper,we study the dissipative control for fractional order systems with time delay.Firstly,the research background and significance of fractional order systems,time delay theory and dissipative theory are introduced,then the developments of fractional order systems with time delay and dissipative theory are introduced.Secondly,the problems of passive and dissipative control for fractional order systems with time delay are studied.The sufficient conditions of passivity and dissipativity for the systems are given by constructing appropriate storage functions and using linear matrix inequality approach.Then the state feedback controller,delayed state feedback controller and the state feedback controller which based observer are designed to make the closed-loop systems passive and dissipative,the feasibility of the theorems is testified by numerical examples.Next the problem of exponentially dissipative control for nonlinear fractional order system with time delay is studied.We obtain the equivalent definition of exponential dissipation for fractional order system which started from the expression of the solution for fractional order system,and we based on the original definition of exponential dissipation for integer order systems and used the related properties of fractional order system.Besides the sufficient conditions of exponentially dissipative control for a class of nonlinear fractional order system with time delay are given.Finally,the main content of this paper is summarized.