Eigenvalue-generalized eigenvector assignment with state feedback

Arbitrary pole placement with the extended Kautsky-Nichols-van Dooren parametric form with minimum gain

“…Where methods [1], [4], [5] all employ parameter matrices of dimension m × n, the parameter matrices in [6] and [7] have dimension n × n. In our recent papers [8]- [9], we gave a novel parametric form for X and F based on the famous pole placement algorithm of Moore [10]. This parameterisation employed parameter matrices of dimension m × n, but required Λ to be diagonal, and hence also assumes the closed-loop eigenvalues have multiplicities of at most m. Very recently in our papers [11]- [12] we generalized this parametric form to accommodate arbitrary multiplicities; the method was based on the pole placement method of Klein and Moore [13]. The principal merit of this approach was to obtain a parameterisation that combines the generality of [6] and [7] with the computational efficiency that comes from an m × n dimensional parameter matrix.…”

A Review on Eigenstructure Assignment Methods and Orthogonal Eigenstructure Control of Structural Vibrations

“…He showed that there is a considerable design freedom beyond the simple pole placement that allows the controller designer to both place the eigenvalues and assign the related eigenvectors; thus, both the speed of response that is determined by the closedloop eigenvalues, and the shape of response that is related to the closed-loop eigenvectors can be controlled. Klein and Moore [4] also presented an algorithm for non-distinct closed-loop eigenvalues and their related eigenvectors keeping the full state feedback scheme by calculating the basis of the null space of the combined system.…”

“…This method identifies the class of achievable eigenvectors and describes explicitly the generalized eigenvectors associated with the assigned eigenvalues. Their approaches to eigenstructure assignment are similar to [3,4]; however, instead of taking an ad hoc approach by identifying the appropriate closed-loop eigenvectors, the design freedom apperas in terms of choosing the appropriate free parameters in the process of finding the state feedback gain matrix. This leads to extra free parameters if the entire open-loop eigenvalues are not required to be moved [7].…”

Finite Dimensional Approximation Theory With Application to Stabilization of Systems With Time Delay

“…The method of eigenvalue and eigenvector assignment with state feedback [3], [4]» as well as simulation of the solution of (5.3) were used to calculate the finite dimensional stabilizing feedback operator.…”