Controllability and nonsingular solutions of Sylvester equations
نویسندگان
چکیده
The singularity problem of the solutions of some particular Sylvester equations is studied. As a consequence of this study, a good choice of a Sylvester equation which is associated to a linear continuous time system can be made such that its solution is nonsingular. This solution is then used to solve an eigenstructure assignment problem for this system. From a practical point view, this study can also be applied to automatic control when the system is subject to input constraints.
منابع مشابه
Adaptive Stabilization of Continuous-time Systems through a Controllable Modified Estimation Model
This paper presents an indirect adaptive control scheme of continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the ...
متن کاملAn explicit solution to right factorization with application in eigenstructure assignment
Based on the well-known Leverrier algorithm, a simple explicit solution to right factofization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback a...
متن کاملSolutions to the generalized Sylvester matrix equations by a singular value decomposition
In this paper, solutions to the generalized Sylvester matrix equations AX−XF = BY and MXN−X = TY with A, M ∈ Rn×n, B, T ∈ Rn×r, F, N ∈ Rp×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × (n + pr). The algorithm proposed in this paper for the euqation AX − XF = BY does not require the controllability of matrix pair...
متن کاملOn the numerical solution of generalized Sylvester matrix equations
The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection metho...
متن کاملAccurate solutions of M-matrix Sylvester equations
This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Sylvester equation AX + XB = C by which we mean both A and B have positive diagonal entries and nonpositive off-diagonal entries and P = Im⊗A+B⊗ In is a nonsingular M -matrix, and C is entrywise nonnegative. It is proved that small relative perturbations to the e...
متن کامل