Canonical forms of linear nonstationary control systems with respect to different groups of transformations (Q1881854)

The author considers the problem of transforming a given linear non-stationary system to a single differential equation, which is called the canonical form of the original system, with respect to a broad class of groups of transformations. Linear changes \(x = G(t)y\) of unknown functions with arbitrary non-singular smooth matrices \(G(t)\) are considered. These transformations conserve the controllability, but in order to retain other properties, such as stability, asymptotic stability, periodicity, almost periodicity, the class of admissible transformations has to be restricted by additional conditions. A description of the sets of systems that have canonical forms with respect to these groups is given in terms of their coefficients.