Observability quadratic normal form for discrete-time systems

This note deals with quadratic observability normal form for nonlinear discrete-time single-input-single-output (SISO) system. First of all, the main concept of quadratic equivalence with respect to the observability property, is introduced for discrete-time systems. Subsequently, normal form structure for discrete time system is developed for system with unobservable linear approximation in one direction. Finally, the effect of the so-called resonant terms on the observer design and synchronization of chaotic systems is pointed out in an illustrative example.