A balanced canonical form for discrete-time minimal systems using characteristic maps Original Research Article

This paper presents a balanced canonical form for the class of discrete-time minimal systems. The main tool is to establish a bijection between the set of minimal systems and the class of minimal discrete-time asymptotically stable systems of the same dimension. This characteristic map is shown to preserve system equivalence and balancing. The canonical form for discrete-time minimal systems is then constructed by mapping the system to its discrete-time asymptotically stable counterpart via the characteristic map, transforming the resulting system to Lyapunov-balanced canonical form, and returning to the original system class by means of the inverse characteristic map.