Robust Dissipative Control For Singular Uncertain Fractional Order Systems With Time-delay

The singular fractional order system,also known as descriptive fractional order system,singular fractional order system or implicit fractional order system,has dynamic characteristics that general fractional order system does not have.For general fractional order systems,the state space model needs to be able to fully characterize the state variables of the system behavior.However,in actual production and life,the system variables selected in the system modeling are often not able to meet the required minimum.In this case,the singular fractional order system model is used to describe the research object.It can be seen that the expression of singular system is more direct and appropriate for practical system.Therefore,it is necessary and meaningful to study generalized fractional order system deeply.In this paper,the problem of dissipative control for singular uncertain fractional order systems with time delay is studied.Firstly,the research background of singular fractional order differential systems and the research significance and development status of dissipative control for singular systems are summarized.Secondly,the problem of passive and dissipative control for singular uncertain fractional order systems with time delay is studied respectively,and the sufficient conditions of passivity and dissipation are given;Then,the derivative state feedback controller and the state feedback controller with time-delay are designed,and the sufficient conditions of passivity and dissipation are obtained by using the method of linear matrix inequality;Thirdly,the passive and dissipative control problems of singular uncertain fractional order systems with time delay based on state observer are studied.The conditions of passive and dissipative control of closed-loop system based on state observer are obtained.The feasibility of the theorem is verified by numerical examples;Finally,the main content of this paper is summarized.