Observers Design For One-Sided Lipschitz Nonlinear Descriptor Systems

In recent years,some state estimation problems which satisfy nonlinear conditions have become an important part of nonlinear system theory.The conventional Lipschitz condition is commonly used in the nonlinear observer design.However,a major limitation in the results for Lipschitz nonlinear systems is that most of the existing design techniques can only stabilise the error dynamics with small Lipschitz constants,but fail to provide a solution when the Lipschitz constants become large.In order to overcome this limitation,the so-called one-sided Lipschitz condition was introduced.For many problems,the one-sided Lipschitz constant is significantly smaller than traditional Lipschitz constant.This makes the one-sided Lipschitz constant more suitable for estimating the effect of the nonlinear part on the system.For this reason,more and more scholars are beginning to work on one-sided Lipschitz conditional research.However,up to now,the design of nonlinear system observers with one-sided Lipschitz conditions has focused on normal systems,there are not many studies in descriptor systems.Therefore,this thesis mainly studies the observer design problem of one-sided Lipschitz nonlinear descriptor systems.This thesis mainly deals with observer design for one-sided Lipschitz nonlinear descriptor systems with the help of the concept of one-sided Lipschitz nonlinear,the concept of quadratic internal boundedness and the method of free weight matrix.The dynamic error equation is used to establish the appropriate Lyapunov function and the proposed class of observers are discussed by Lyapunov stability theory.The main research work are as follows:1.For the discrete-time nonlinear descriptor system with one-sided Lipschitz condition,a full-order state observer and a reduced-order observer are proposed.By selecting the Lyapunov function,using Schur complement lemma,one-sided Lipschitz nonlinear condition and quadratic internal bounded concept to construct the existence conditions for the full-order observer and the reduced-order state observer.Finally,the simulation examples are given to illustrate the validity of the results.2.For the continuous-time nonlinear descriptor systems with one-sided Lipschitz nonlinear model.Firstly,the proportional observer design of continuous-time descriptor system is given.Secondly,by using the method of free-connection weighting matrices,the proportional and derivative observer of continuous-time descriptor system is constructed.The sufficient conditions for the asymptotic stability of the error dynamics are obtained and the design method of the gain matrix is given.Then an observer-based controller is then presented.Finally,the above theory is verified by simulation results.3.For the continuous-time descriptor system model with actuator fault,the proportional derivative learning observer design for continuous-time descriptor systems is given by using Lyapunov stability theory and free weight matrix method.Based on the linear matrix inequality,the sufficient conditions for the existence of the learning observer and the design method of the gain matrix are obtained.Then,the result is generalized to a nonlinear descriptor system with a one-sided Lipschitz condition,and a sufficient condition for the asymptotic stability of the error dynamics is obtained.Finally,numerical examples are provided to show the effectiveness and applicability of the theoretical results.