Some analysis problems of the linear systems




controllability, observability, canonical form, descriptor, linear system


New approaches to the transformations of the uncontrollable and unobservable matrices of linear systems to their canonical forms are proposed. It is shown that the uncontrollable pair (A,B) and unobservable pair (A,C) of linear systems can be transform to their controllable (A,B), and observable (A,C) canonical forms by suitable choice of nonsingular matrix M satisfying the condition M[AB]=[AB] and M=[A,B] , respectively. It is also shown that by suitable choice of the gain matrix K of the feedbacks of the derivative of the state vector it is possible to reduce the descriptor system to the standard one.


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