The Study And Design Of Observer With Lipschitz Constraint

Quantity of state in nonlinear system is a difficult problem in modern control technology. Therefore, the design of systematic observer has become a hot issue of control system and signal processing. there exit many ways on the design of the observer,the design of the observer on a linear system is relatively simple,while the design of the observer on a non-linear system is more complex. This paper gives the design of the observer for a class of a continuous-time descriptor system and an adaptive system with Lipschitz constraint including a full-order observer and a reduced-roder observer.For a class of a continuous-time descriptor systems with Lipschitz constraint which is a function which is dependent on the system state and the system input, the paper considers if Riccati equation has a solution, there exists a full-order observer and a reduced-roder observer with this continuous-time discriptor system, a approach is developed. Through the way of linear matrix inequality, give the design of a full-order observer and a reduced-roder observer and ite design of oserver depends on the solution of linear matrix inequality. Through linear matrix inequality give the design of an adaptive full-order observer and an adaptive reduced-order observer. Some illustrative examples are presented to show the effectiveness of the proposed approach. meanwhile, a robot control system is given in a engineering application, in the actual system we only give one of a full-order observer and a reduced-order observer. In order to compare linear matrix inequality and Riccati equation,the full-order observer of a robot system based on a linear matrix inequality and Riccati equation is given.Through the linear matrix inequality and Riccati equation the applicability of above-mentioned two methods is strong for the design of the observer for a class of a continuous-time descriptor systems with Lipschitz constraint, especially the linear matrix inequality, not only gives the design of a class of a continuous-time descriptor systems with Lipschitz constraint, but also are expected to give the design of the observer for a more complex continuous-time descriptor systems with Lipschitz constraint and adaptive systems,time-delay system. While, the linear matrix can be used to research the H_∞characteristics.