Computationally efficient state-feedback stabilizability determination in switched linear systems with rank-one modes

The present paper is concerned with state-feedback stabilizability of discrete-time switched linear systems whose modes are described by rank-one matrices. Necessary and sufficient conditions for state-feedback exponential stabilizability, in this class of switched systems, are presented. It is shown that, a switched linear system, whose modes are described by rank-one matrices, is state-feedback exponentially stabilizable if and only if an associated set of matrices includes a member having spectral radius smaller than one. A numerical example provides illustration.