An algorithm to check the nonnegativity of singular systems (original) (raw)

Numerical Algorithms for Inverse Eigenvalue Problems Arising in Control and Nonnegative Matrices

2006

An Inverse Eigenvalue Problem (IEP) is to construct a matrix which possesses both proscribed eigenvalues and desired structure. Inverse eigenvalue problems arise in broad application areas such as control design, system identification, principle component analysis, structure analysis etc. There are many different types of inverse eigenvalue problems and despite of a great deal of research effort being put into this topic many of them are still open and are hard to be solved. In this dissertation, we propose optimization algorithms for solving two types of inverse eigenvalue problems, namely, the static output feedback problems and the nonnegative inverse eigenvalue problems. Consequently, this dissertation is essentially composed of two parts. In the first part, three novel methodologies for solving various static output feedback pole placement problems are presented. The static output feedback pole placement framework encompasses various pole placement problems. Some of them are NP...

Reversibility on the Set of Singular Matrices

Singularity poses a big hindrance in the study of matrices as no meaningful analysis can be done without making reference to matrix inverse. In this paper, an attempt is made to survey some properties of singular matrices in an effort to reduce to the bearest minimum or to terminate the effects of singularity in matrix algebra.

Testing Functional Output-Controllability of Time-invariant Singular Linear Systems

After introducing the concept of functional outputcontrollability for singular systems as a generalization of the concept that is known for standard systems. This paper deals with the description of a new test for calculating the functional output-controllability character of finite-dimensional singular linear continuous-timeinvariant systems in the form Ex_ (t) = Ax(t) + Bu(t) y(t) = Cx(t) } (1) where E,A ∈ M = Mn(C), B ∈ Mn�m(C), C ∈ Mp�n(C). The functional output-controllability character is computed by means of the rank of a certain constant matrix which can be associated to the system.