A Parametric Design Method Of Luenberger Observer For Time-delay Systems And Applications

Time-delay phenomena exist widely in all kinds of natural systems,such as aerospace systems,chemical process systems,networked control systems,etc.The existence of time-delay may lead to poor or even unstable system performance indicators,so the related control problems of time-delay systems have received wide attention.However,in many practical systems,for the sake of economy,difficulty,and practicality of measurement,it is difficult to get all the state information of the system,so it is necessary to design observers for state reconstruction.In this paper,a parametric design method of the function observer is presented.Based on the solution of the generalized Sylvester equation,a general parameterized form of the function observer is established.Using the parameterized method,the observer dynamic error system can be transformed into a linear constant system with the expected characteristic structure.At the same time,based on the free parameters provided by the parameterized method,the convergence speed of the observer error system can be controlled.In addition,the parameterized design method of the interval observer for time-delay system functions is studied,which fills in the blank of relevant research.The main work of this paper is as follows:1.For a class of linear stationary systems with time delay,the design of the function observer is studied and a parameterized design method is presented.The problem of observer design is transformed into a problem of solving a class of Sylvester matrix equation.By making full use of the degree of freedom in the parameterized method,the problem of constraints in the observer coefficient matrix is effectively solved.The observer designed does not contain time-delay terms and has a lower order,which effectively reduces the complexity of the observer design.2.For a type of linear time-varying systems with time-delay,the design of the function observer is studied and a parameterized design method is presented.By constructing an appropriate Lyapunov-Krasovskii functional and using linear matrix inequality,the stability of the observer dynamic error system is effectively guaranteed.At the same time,the design problem of the function observer is transformed into a solution problem of a set of differential equations,which avoids complex transformations and can control the convergence speed of the observer error system.It is suitable for most linear time-varying systems with time delay.3.For a class of linear time-delay systems with input and output disturbances,the design problem of the functional interval observer is studied and a parameterized design method is presented.By constructing a novel form of the function interval observer and using the parameterized solution of the Sylvester matrix equation,the parameterized design of the interval function observer is implemented,and a detailed design algorithm is provided.Based on the purpose of the design,the existence condition and design method of the functional interval observer are presented and considered for the first time in this paper.The designed observer has a more general structure,which is suitable for systems with multiple time delays,and realizes the interval estimation of time delay systems with disturbances.4.For a type of linear time-varying systems with disturbances and time delays,the design problem of the functional interval observer is studied and a parameterized design method is presented.By constructing a novel form of functional interval observer and using the parameterized solution of the time-varying Sylvester matrix equation,the general fully parameterized form of the observer is obtained.The form and design method of the functional interval observer for the system are first proposed and considered in this paper.Interval estimation for linear time-varying systems with both perturbation and time delay is achieved.A new idea for interval design is provided,which complements the parameterized design method and theory of function observer for time-delay systems.