A. Roca

Invariant factor assignment under state feedback and output injection

For a given system (A,B,C) necessary and sufficient conditions are given to assign invariant factors to the matrix of the system performing a state feedback and an output injection, over an arbitrary field.

Decoding a Perturbed Sequence Generated by an LFSR

Given a sequence of bits produced by a linear feedback shift register (LFSR), the Berlekamp-Massey algorithm finds a register of minimal length able to generate the sequence. The situation is different when the sequence is perturbed; for instance, when it is sent through a transmission channel. LFSRs can be described as autonomous systems. A perturbed sequence of bits generated by an LFSR can be interpreted as a codeword in the binary linear code generated by the corresponding observability matrix. The problem of finding the original sequence can then be stated as the decoding problem, “given the received codeword, find the information transmitted”. We propose two decoding algorithms, one based on a brute force attack and the other one based on the representation technique of the syndromes introduced by Becker, Joux, May, and Meurer (2012).

Restricted invariant factor assignment under state-feedback☆

Abstract For a given matrix pair (A, B), A square, necessary and sufficient conditions are established for the existence of a state feedback matrix F such that A + BF is in the same similarity class as a partially prescribed square matrix.