Guaranteed Performance Control Of Uncertain Time-delay LPV System

As an important time-varying system,the linear parameter-varying system(Linear Parameter-Varying systems)has a state space matrix as a function of determining some time-varying parameters.Although these parameters are unknown,they are all real-time measurable.Linear parameter-varying system has been widely used in practical engineering,such as fighter aircraft,missile automatic navigation system,robot control,flight control system and so on.Because the system in practice often contains nonlinear and time-varying characteristics,it will cause errors between the controlled object and the established system.With the development of science and technology and the deepening of research,the emergence of linear parameter-varying system solves this problem well.In practical modeling,there are structural uncertainties,and the phenomenon of delay will also affect the performance of a system.As a result,it is very important to study the LPV system deeply.Aimed at studying the performance-preserving control problem of uncertain time-delay LPV system,the paper is as follows:The first chapter briefly introduces the significance and stability of LPV system,the related contents and the current research situation at home and abroad.Secondly,the relevant definitions and theorems of this paper are given.Finally,the mathematical symbols used in this paper are given.Chapter 2 analyzes the robust stability of time-delay LPV systems with structural uncertainties.Through the method of constructing Lyapunov functional and using Schur Complement lemma to deal with matrix inequality,sufficient conditions for robust stability of the system are obtained.Secondly,the performance index is introduced to control the performance of the system,and the sufficient conditions of robust stability and satisfying the performance index are obtained.By using the properties of Schur complement and elementary transformation,the sufficient conditions are transformed into solvable linear matrix inequalities.Chapter 3 deals with robust state feedback performance control for uncertain time-delay LPV systems.Because the state vector in some systems is not easy or can-not be measured directly,in order to realize the need of state feedback,the state input feedback controller is designed on the basis of the second chapter,so as to effectively improve the performance of the control system.By constructing the Lyapunov functional,the matrix inequality is processed,and the system is controlled to ensure the performance.The sufficient conditions for the robust stability of the closed-loop system satisfying the performance index is obtained,as well as the controller gain matrix which makes the system reach a stable state.The fourth chapter discusses the problem of dynamic output feedback performance control based on the second chapter.During the treatment of nonlinear matrix inequality,a new set of matrix variables is introduced by variable substitution method,which is transformed into a block linear matrix inequality represented by new variables,and the results of variables are obtained by using the LMI toolbox.Then the value of the original variable is obtained by using the substitution relationship between the old and new variables.