Interval Observers Design For Singular Systems With Matrix Perturbation And Interference

Observer design has always been an important research topic in the field of control theory.Scholars domestic and overseas have proposed many observer design methods,such as Luenberger observer,adaptive observer and so on.The accuracy of these observer depends on integrity of the system model.It is difficult for designed observers to reconstruct the state of the system accurately,when the system is not measurable or there is unknown disturbance and measurement noise.In these cases,it is a good way to ensure the accuracy of reconstructed state system by designing interval observer.The interval observer has important theoretical research significance and practical application value.The interval observer design problems for singular systems with matrix perturbation and disturbances are investigated in this paper.The main research contents are as following:Firstly,the basic concept of interval observer,common lemma and basic design method are given.A basic interval observer is designed for a class of linear systems,and a transformation method is given to transform the dynamic system of observation error into a positive system.In addition,an interval observer is designed for a class of linear systems with disturbance,and the method of dealing with the disturbance term is given.Secondly,an interval observer is designed for a class of singular system with unknown disturbance,measurement noise and nonlinear terms.The disturbance and measurement noise of the system are assumed to be unknown but bounded.The equivalent system of observation error dynamic system is given in this paper.Besides,the necessary and sufficient condition for observation error dynamic system to be positive,the existence condition of interval observer for singular system and the bounded stability condition for observation error dynamic system are given.At last,the simulation results are given through the numerical examples to verify the effectiveness of the algorithm we proposed.Finally,another interval observer is designed for a class of linear singular system with unknown disturbance,measurement noise and matrix perturbation in the system matrix.The method of dealing with the uncertainty in the system matrix and the condition of the existence of the interval observer are given.Assuming the disturbance and measurement noise are unknown but bounded,the candidate interval observer is given byrank condition.And the existence condition of interval observer is given based on the positive analysis for the observation error dynamic system of candidate interval observer.At the same time,the stability condition of observation error dynamic system is given based on the stability analysis of the interval observer.Finally,the numerical simulation examples of the interval observer,and the simulation results are provided to verify the effectiveness of the algorithm.