Exponential representations for linear systems

Two aspects of the theory of exponential representation for the solution of linear differential equation systems are investigated. The first result for (2; 2)-order systems develops a relationship between the exponents of the system representation and a solution of an appropriately defined Riccati equation. A similar result is known for classical representations, thus providing a direct connection between the two theories. Second, as a collateral result, it is shown that the global invertibility of the defining exponential relationships does not necessarily imply that the representation is global.