Robust Stabilization And H-inf Control Of Commensurate Fractional Muli-Order Uncertain Systems

In this subject,robust stabilization and H-inf control methods are studied for commensurate fractional multi-order system with norm-bounded uncertainties.Directly derived from the commonly used integral multi-order system,the fractional multi-order system is obtained by multiplying the different integer orders with a common fraction ranging between 0 and 2.Especially,norm-bounded uncertainties are taken into consideration to describe the dynamic process of the system in practical application more accurately.Finally,the research object of the subject is established: commensurate fractional multi-order uncertain systems.The research methods change with the value range of the minimum nonzero order of the multi-order system.This subject mainly focuses on the case with the minimum non-zero order ranging between 0 and 1,and carries out robust stabilization and H-inf control research on the above system by means of linear matrix inequality,which is a common tool for studying fractional order systems.The specific research contents of this subject are as follows:Firstly,the multi-order system studied in this subject is described in detail.Relevant definitions and assumptions are introduced to simplify the subsequent research.At the same time,by referring to the existing transformation methods for multi-order integer order system with uncertain description,the original multi-order systems studied are transformed into the fractional order state-space system.Secondly,the existing stability theory and different stabilization methods of fractional order systems are applied to the state-space system.Based on the state-space system,the sufficient conditions for the stability of the original multi-order system and state feedback controller design methods are studied.Thirdly,on one hand,a static output feedback controller based on the partially measurable state vector of the state-space system is proposed.On the other hand,the state observer-based controller design method is introduced to stabilize the system when the state vector of the state-space system is not directly measurable.Finally,based on the possible perturbation of system environment as well as the system uncertainties,different H-inf norm-based controllers are designed to stabilize the state-space system,as well as reduce the influence of external disturbance on the state-space system,thus optimize the performance of the original multi-order system and enhance the applicability of the theory.What’s more,all results are presented in the form of linear matrix inequality to take advantages of the LMI mathematical tools.Besides,numerical examples are implemented to verify the reliability and feasibility of the theories presented in the research.