Delay Systems, Observer Design,

The substance of the Singular Time-delay System's observer:for the being observerd system∑of given Singular Time-delay System, construct a system with the same property with the∑. Making use of input value u and output value y which are directly measured in∑to be input value of∑. and also to make the state of E or changed form x asymptotically equivalent to∑'s state x. The researchers made lots of study on observer of Linear Singular Time-delay System and gained great progress. Many design solutions adopts the method of linear matrix inequalities(LMIs), but the solving procedure of coefficient matrix in these solutions is too complex and is with large amount of calculation. This paper adopts the eigenvalue assignment which based on the Lambert W function and studies the Liner Singular Time-delay System's observer and designs the Finite-Time Observer. Finally, for the obvious dual construction occurred in dynamic observer and liner output feedback controller design solution design the construction solution for dynamic observer. The dynamic observer can be considered as the expansion of static observer.The research findings of this paper are showed in the following:(1)Design of full-order normal observer for singular time-delay system. Based on the research on eigenvalue-assigning technology, the paper introduces a brand-new linear full-order normal observer of linear singular time-delay system. Finally, the paper uses Matlab to simulate a particular example, and uses simulink to validate its practicability. Simulation result shows the system's dynamic error state is asymptotically stable, and therefore this method is practical and effective.(2)Design of finite-time normal observer for linear singular time-delay system, which converges in finite time exactly. The observer comprises two infinite-time observers and a finite delay element. Based on the research on eigenvalue-assigning technology, the paper introduces a brand-new linear full-order normal observer of linear singular time-delay system. Finally, the paper uses Matlab to simulate a particular example, and uses simulink to validate its practicability. Simulation result shows this method is practical and effective.(3)The dynamic observer design of Liner Singular Time-delay System. The dynamic observer, namely, is the condition variable of observer containing the dy-namic variablities. The dynamic observer can be considered as expansion of static observer. The observer design is the dual of condition feedback design. Based on this concept, putting forward one design of dynamic observer, and the dynamic observer constructed conforming to the requirement shall meet the seperability theorem.