The Structural Decomposition For Singular Systems And Its Applications

The structural canonical form representation plays a useful role in the anal-ysis and control of linear systems.So does the decomposition approach for singular linear systems.It is a technique dealing with a system by transforming its state,input and output variables such that the system under the new coordinate is decomposed into forms with special structural properties.Singular systems are governed by the so-called singular differential equations, therefore the systems have many special features that are not found in proper linear systems.In this thesis,the structural properties,feedback control problem,geometric subspaces and disturbance decoupling by output feedback for singular systems are investigated based on the structural decomposition approach for singular systems.The major contributions of this thesis are as follows:1.The key idea of Special Coordinate Basis decomposition for proper systems is analyzed.Some geometric invariant subspaces of proper systems are discussed to show that the transformed system is capable of explicitly displaying such invariant subspaces.2.New algorithm and further decomposition are presented for the structural decomposition of singular systems based on the SCB decomposition and the original method.Under the new decomposition proposed,some subsystem of the transformed system is simplified and the supremal outputnulling(A.E,Im(B))-invariant subspace of singular systems can be clearly expressed in an explicit form.3.The properties of singular systems,including controllability,observability, stabilizability,detectability,normal rank,invariant zeros and invertibility, are discussed and related feedback controls are studied to eliminate the impulse term in the state response of singular systems.4.The supremal output-nulling(A,E,Im(B))-invariant subspace of singular systems is studied to give its clear expression under the structural decomposition of singular systems.5.The disturbance decoupling by output feedback for regular singular sys- tems with left invertibility is discussed.The necessity and sufficient condition for the solvability of the above disturbance decoupling problem is proposed and a method to get such an feedback gain by solving linear equation groups is presented.