The stabilization problem of positive linear discrete-time systems (PLDS) by linear state feedback is considered. A method based on a Brauer's theorem is proposed for solving the problem. It allows us to modify some eigenvalues of the system without changing the rest of them. The problem is studied for the single-input single-output (SISO) and for… (More)
An n × m real matrix A is said to be totally nonpositive (totally negative) if every minor is nonpositive (negative). In this paper, we study characterizations of these classes of matrices by minors, by their full rank factorization and by their thin QR factorization.
In this paper, a method is given that obtains a full rank factorization of a rectangular matrix. It is studied when a matrix has a full rank factorization in echelon form. If this factorization exists, it is proven to be unique. Applying the full rank factorization in echelon form the Flanders theorem and its converse in a particular case are proven.
An n × n real matrix A is said to be (totally negative) totally nonpositive if every minor is (negative) nonpositive. In this paper, we study the properties of a totally nonpositive matrix and characterize the case of a nonsingular totally nonpositive matrix A, with a 11 < 0 in terms of its LDU factorization (L(U)) is a unit lower-(upper-) triangular… (More)
The transfer functions of discrete-time SISO compartmental systems whose compartments are connected either in series or in parallel are characterized, and then the corresponding realization problem is studied. The obtained results are extended to the transfer matrix of N-periodic compartmental systems.