6. Basic changes

Whether at the level of the black box or the overall system, we have seen that a number of state representations are possible. Although they are all theoretically equivalent, we may be led to prefer particular representations, especially at the level of the matrix A, either because they better highlight the modes – or the global characteristic polynomial – or because they shed light on the fundamental structure of the system – or because they require far fewer elements to be kept in memory. These include representations where the matrix A is diagonal – or block-diagonal – or in companion form.

Given an initial representation where the matrix A is arbitrary, finding a transformation