Introduction E IGENSTRUCTURE assignment algorithms are widely used to design control systems.Most of the available eigenstructure assignment algorithms assign all of the eigenvalues to the desired values.The eigenstructureassignmentalgorithmcan be dividedinto two groups, that is, the null space approach and Sylvester equation approach.The null spaceapproachis used to solvemode decoupling proble...

Recent ScaLAPACK-style implementations of the BartelsStewart method and the iterative matrix-sign-function-based method for solving continuous-time Sylvester matrix equations are evaluated with respect to generality of use, execution time and accuracy of computed results. The test problems include well-conditioned as well as illconditioned Sylvester equations. A method is considered more genera...

In this paper, the eigenvalues of various non-Sylvester Hadamard matrices constructed by monomial permutation matrices are derived, which shows the relation between the eigenvalues of the newly constructed matrix and Sylvester Hadamard matrix. * The authors are with School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea, ([email protected]). Paper No....

A complete parametric approach is proposed for the design of the Luenberger type function Kx observers for descriptor linear systems. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, parametric expressions for all the coefficient matrices of the observer are derived. The approach provides all the degrees of design freedom, which can be utilized to ac...

Fixed-order controller design for LTI-SISO polytopic systems is investigated using rank deficiency constraint on the controller Sylvester resultant matrix. It is shown that the non-convexity of fixed-order controller design problem can be contracted in a rank deficiency constraint on Sylvester resultant matrix of the controller. Then, an improved convex approximation of the rank deficiency cons...

Exponential time integrators are well-established discretization methods for semilinear systems of ordinary differential equations. These use ? ? functions, which matrix functions related to the exponential. This work introduces an algorithm speed up computation function action over vectors two-dimensional (2D) matrices expressed as a Kronecker sum. For that, we present auxiliary exponential-re...

James Joseph Sylvester coined the term “matrix” and contributed much to the early development of matrix theory. To mark the 200th anniversary of his birth I show how Sylvester’s work on matrices continues to influence applied mathematics today.