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The parametric design problem for eigenstructure assignment with arbitrary expected state vector is studied via state feedback in linear time invariant systems. The main idea of the considered problem is to design a parametric form of the state feedback, so that the designed closed-loop system has the desired eigenvalues, the desired eigenvectors and arbitrary expected state vector. Based on the parametric solution for a class of Sylvester matrix equation, the parametric expression of all the state feedback gain matrices is given in this paper. The free parameters including in the state feedback gain matrix can be further used to meet other performance requirements for the control system design. Finally, a simulation experiment is given to illustrate the effectiveness and simplicity of the proposed parametric method for the state feedback eigenstructure assignment problem with arbitrary expected state vector in the linear time invariant systems.

A Parameter Eigenstructure Assignment Design with Any Desired State Vector in Linear Time-Invariant System