Descriptor system theory has become an important part of control system theory.Compared with the standard state-space systems,the singularity of the derivative matrix of descriptor systems is a source of its special characteristics.Therefore,it is significant to research its derivative matrix.In practical physical systems,due to the limitation of measurements or other factors,it is difficult to directly obtain some or all of the system states.Therefore,the design of observer has attracted the attention of many scholars.The proposed proportional-derivative state observer,whose derivative matrix is nonsingular,is more practical in physics and more robust compared with the usual proportional observer of descriptor systems.In this thesis,by using the method of free-connection weighting matrices and the technique of linear matrix inequality,the problem of designing proportional-derivative observer for descriptor systems and its application is studied,which is motivated by the descriptor system theory and T-S fuzzy system theory.The main results are summarized as follows:(1)The design of proportional-derivative observer for discrete-time descriptor systems is discussed.Several equivalent necessary and sufficient conditions for the existence of a proportional-derivative state observer are proposed,and the specific calculation method of proportional gain and derivative gain is also given by using the linear matrix inequality technique.Moreover,based on the proposed observer design method,a sufficient condition which ensures the error system to be asymptotically stable is obtained by extending the linear theory to a class of discrete-time nonlinear descriptor systems,where the nonlinearity is assumed to satisfy Lipschitz constraint.It is worth pointing out that the proportional gain and derivative gain can be given simultaneously by using the proposed technique in this thesis,which is different from ones in the existing literature.(2)The design of proportional-derivative observer for continuous-time descriptor systems with time-delay is investigated.With the help of free-connection weighting matrices and Lyapunov stability theory,a sufficient condition which ensures the error system to be asymptotically stable is obtained.Furthermore,the proposed observer design method is further extended to a class of nonlinear descriptor systems,where the nonlinearity is assumed to satisfy Lipschitz constraint.All the conditions are expressed as linear matrix inequality,which can be easily verified.Finally,the proposed proportional-derivative observer is applied to sensor fault estimation.It is worth pointing out that the sensor fault considered in this thesis has no additional restrictions,which is different from ones in the existing literature.(3)The design of proportional-derivative observer for T-S fuzzy descriptor systems is researched.According to the available knowledge on the premise variables,first,observer design with measurable premise variables is considered,and a sufficient condition is obtained,which ensures the error system to be asymptotically stable.Next,the design of proportional-derivative observer with unmeasurable premise variables is studied by assuming the perturbation term to be bounded.However,the considered perturbation term on the estimation error depends on the input,which means a large value of the input bound leads to a large value of the perturbation bound.Then,in this case the LMI may be infeasible.Therefore,another method for the design of observer with unmeasurable premise variables is proposed.Finally,the proposed proportional-derivative observer is applied to sensor fault estimation. |